Become A Master of Some Applications of Trigonometry

High school math that covers Trigonometry - Heights & Distances in detail, with a step-by-step approach with formulae.

Created byLakshmi Narayana

Last updated 11/2022

English

What you'll learn

Review of Concepts Trigonometric Ratios.
Heights and Distances.
Line of Sight, Angle of Elevation and Angle of Depression.
Solving different real-life situations involving Heights and Distances by using Trigonometry.
At the end of the course, students will not only have learned about the topics in detail but also be able to solve various problems based on them.

Course content

6 sections • 38 lectures • 4h 43m total length

Introduction14:06
Introduction:
Q 13:20
If the length of the shadow of a tower is equal to its height,
then the angle of elevation of the sun is:
Q 24:02
If a tower 30m high casts a shadow 10√3m long on the
ground, then what is the angle of elevation of the sun?
Q 36:34
An observer 1.5 m tall is 28.5 m away from a tower 30 m high. Find the angle of elevation of the top of the tower from his eye.
Q 43:40
The figure shows the observation of point C from point A. Find the angle of depression from A, if AB = 4 cm and BC = 4
Test your understanding
Home Assignment

Introduction2:02
Problems based on finding one side of right angled triangle when an acute angle and one of the other two sides are known.
Q 15:30
A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.
Q 28:45
An electrician has to repair an electric fault on a pole of height 5 m. She needs to reach a point 1.3m below the top of the pole to undertake the repair work (see Fig.). What should be the length of the ladder that she should use which, when inclined at an angle of 60° to the horizontal, would enable her to reach the required position? Also, how far from the foot of the pole should she place the foot of the ladder? (You may take √3 = 1.73)
Q 38:29
A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30o with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 meters. Find the height of the tree.
Q 43:47
A ladder 15 m long leans against a wall making an angle of 60o with the wall. Find the height of the wall from the point the ladder touches the wall.
Test your understanding
Home Assignment

Introduction2:31
Problems based on two right angled triangle having common base (common horizontal line) or perpendicular (common vertical line)
Q 15:00
An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?
Q 29:00
From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff and the distance of the building from the point P. (You may take √3 = 1.732)
Q 36:47
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.
Q 47:39
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30∘ and that of the top of the flagstaff is 600. Find the height of the tower.
[Use √3 = 1.732.]
Test your understanding
Home Assignment

Introduction1:39
Problems based on use of two right angled triangles when length of one side of each triangle are equal or a relation between them is known:
Q 112:57
The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings.
Q 210:59
The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 30 seconds, the angle of elevation changes to 30°. If the jet plane is flying at a constant height of 1500 m, find the speed of the jet plane.
Q 39:31
The angle of elevation of the top of a vertical tower from a point on the ground is 600. From another point 10m vertically above the first, its angle of elevation is 300. Find the height of the tower.
Test your understanding
Home Assignment

Introduction1:20
Problems based on right angled triangle formed by the angle of depression.
Q 15:44
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.
Q 27:57
A peacock is sitting on the top of a tree. It observes a serpent on the ground making an angle of depression of 30°. The peacock catches the serpent in 12 s with the speed of 300 m/min. what is the height of the tree?
Q 39:51
The angle of elevation of a cloud from a point 120 m above a lake is 300 and the angle of depression of its reflection in the lake is 600. Find the height of the cloud.
Q 49:07
Two ships are approaching a light house from opposite directions. The angle of depression of two ships from top of the light house are 300 and 450. If the distance between two ships is 100 m. Find the height of light-house.
Test your understanding
Home Assignment

Q 14:25
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°
(see Fig. 9.11).
Q 28:18
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Q 39:06
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
Q 44:37
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
Q 55:15
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
Q 611:23
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
Q 78:34
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
Q 810:46
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
Q 98:00
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
Q 1011:50
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.
Q 1110:38
A TV tower stands vertically on a bank
of a canal. From a point on the other
bank directly opposite the tower, the
angle of elevation of the top of the
tower is 60°. From another point 20 m
away from this point on the line joing
this point to the foot of the tower, the
angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal.
Q 128:19
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Q 1310:53
As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
Q 1411:16
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

Requirements

Elementary knowledge of basic fundamental operations.
Elementary knowledge of Trigonometric Ratios.
Each chapter is inbuilt with prerequisite knowledge classes where the child gets immense knowledge and a clear understanding of the chapters.

Description

This course is intended for underage students. The course can only be purchased by parents, and students must watch under the supervision of an adult parent. This course is carefully designed to explain various applications of Heights and Distances by using Trigonometry.
It has 38 lectures spanning around 5 hours of on-demand videos that are divided into 5 sessions. The course is divided into a simplified day-by-day learning schedule.
Each topic is divided into simple sessions and explained extensively by solving multiple questions. Each session contains a detailed explanation of the concept.
An online test related to the concept for immediate assessment of understanding.
Session-based daily home assignments with a separate key. The students are encouraged to solve practice questions and quizzes provided at the end of each session.
This course will give you a firm understanding of the fundamentals and is designed in a way that a person with little or no previous knowledge can also understand very well.
It covers 100% video solutions of the NCERT exercises , with selected NCERT exemplars and R D Sharma.
Our design meets the real classroom experience by following classroom teaching practices. We have designed this course by keeping in mind all the needs of students and their desire to become masters in math. This course is designed to benefit all levels of learners and will be the best gift for board-appearing students. Students love these easy methods and explanations. They enjoy learning maths and never feel that maths is troublesome.

Topics covered in the course:

Review of Concepts Trigonometric Ratios.
Heights and Distances
Line of Sight
Angle of Elevation
Angle of Depression
Solving different real-life situations involving Heights and Distances by using Trigonometry.

With this course you'll also get:

Improve your math skills by using trigonometry to solve height and distance problems.
A Udemy Certificate of Completion is available for download.

Feel free to contact me with any questions or clarifications you might have.

I can't wait for you to get started on mastering the real number systems.

I look forward to seeing you on the course! :)

Benefits of Taking this Course:

On completion of this course, one will have detailed knowledge of the chapter and be able to easily solve all the problems, which can lead to scoring well in exams with the help of explanatory videos ensure complete concept understanding.

Downloadable resources help in applying your knowledge to solve various problems.

Quizzes help in testing your knowledge. In short, one can excel in math by taking this course.

Who this course is for:

This course has been designed for students of the Grade 10th CBSE, ICSE, SSC, GCSE, IGCSE, SAT, ACT, GRE, and other board-appearing students.
Students studying for the public or other competitive examinations.
Home-school parents are looking for extra support with the fundamentals.
For 11th, 9th, and 8th grade students, this will help as a bridge course.
Anyone interested in revising or learning the basics of mathematics should.
Students in junior high and high school/secondary schools.
Anyone who wants to proficient mathematics and the Solving different real life situations on Hights and Distances by using Trigonometry well.
Anyone who wants to study math for fun after taking a break from school.
It will also benefit schools who wish to run classes in the absence of a teacher and make learning fun for their students.
It will also benefit teachers and schools who wish to improve their teaching skills and make learning fun for their students.

Become A Master of Some Applications of Trigonometry

What you'll learn

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Course content

Session-15 lectures • 32min

Session-25 lectures • 29min

Session-35 lectures • 31min

Session-44 lectures • 35min

Session-55 lectures • 34min

Exercise 9.114 lectures • 2hr 3min

Requirements

Description

Who this course is for: