Practice Questions for Some Application of Trigonometry

Question 1: A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the remaining height of the tree. 

Solution:

 

Step 1: The angle in the question is 30°, and the distance is 8m. 

Step 2: On looking upon the statement, the diagram can be viewed as shown below. A triangle ABC, is formed, where, ∠BAC, is 30°, and AC is 8m. We, need to find the height i.e. BC. 

Step 3: As, mentioned earlier only two formulas, are used for the entire chapter, i.e. of sine and tan. In this question, we need to find, the perpendicular distance from the given angle, so tan is used. 

⇒ BC = 4.624. 

Hence, the remaining height of the tree is 4.624m. 

Question 2: 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 10m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°.  Find the height of the tower and the width of the canal.

Solution: 

 

Step 1: The angle in the question is 30°, 60° and the distance is 10m.

Step 2: On looking upon the statement, the diagram can be viewed as shown below. A triangle ABC, is formed, where, ∠ABC, is 30°, ∠ADC, is 60°and AC is 10m. We, need to find the height i.e. DC, and AC. 

Step 3: As, mentioned earlier only two formulas, are used for the entire chapter, i.e. of sine and tan. In this question, we need to find, the perpendicular distance from the given angle, so tan is used.

Hence, the height of the tower is  m. and width of the canal is 5 m.

Question 3: 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 45°. If the tower is 25 m high, find the height of the building.

Solution:

 

Step 1: The angle in the question is 30°, 45° and the height of the tower is 25m.

Step 2: On looking upon the statement, the diagram can be made as shown below. Two traingles ABD, and CBD are formed. CD = 25, ∠CBD = 45°, and ∠ADB = 30°, AB = ?. 

Step 3: Calculate the length BD, then apply tan formula, to calculate AB. 

Hence, the height of the building is 14.45m. 

Question 4: From the top of a 6 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 30°. Determine the height of the tower, from the foot.

Solution: 

 

Step 1: The angle in the question is 60°, 30° and the height of the building is 6m.

Step 2: On looking upon the statement, the figure is made as shown below, where, ∠BAC = 60°, ∠DAC = 30°, AE = 6m, BD = ?. 

Step 3: Calculate the length ED, then apply tan formula, to calculate BD.

 

Hence, the height of the tower from the foot is 24m. 

CBSE Class 10 Maths Notes Chapter 9 Applications of Trigonometry are an excellent resource, for knowing all the concepts of a particular chapter in a crisp, and friendly manner. Our articles, help students learn in their language, with proper images, and solved examples for better understanding the concepts. 

Chapter 9 of the NCERT Class 10 Maths textbook delves into the world of Applications of Trigonometry used in real life and covers various topics such as understanding the angle of elevation, angle of depression, and line of sight. These notes are designed to provide students with a comprehensive summary of the entire chapter and include all the essential topics, formulae, and concepts needed to succeed in their exams.