Chapter 13: Q42. (page 707)

A surveyor stands $100 feet$ from a building and sights the top of the building at a $55 °$ angle of elevation. Find the height of the building.

Short Answer

Expert verified

The height of the building is $142.8 feet$ .

Step by step solution

Step 1. Write down the given information.

Considering that the height of the building is AB and the surveyor stands 100 feet away at point C from the building (AB) as shown below.

Step 2. Calculation.

Apply trigonometric ratios in triangle ABC to find the height (AB) of the building. Therefore, in triangle ABC,

$\begin{matrix} \frac{A B}{B C} = \tan (55 °) \\ A B = B C \tan (55 °) \\ A B = 100 \tan (55 °) \\ A B = 142.8 feet \end{matrix}$

Since $A B = 142.8 feet$ , hence the height of building is $142.8 feet$ .

Step 3. Conclusion.

The height of the building is $142.8 feet$ .

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A surveyor stands $100 feet$ from a building and sights the top of the building at a $55 °$ angle of elevation. Find the height of the building.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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A surveyor stands 100feet from a building and sights the top of the building at a 55° angle of elevation. Find the height of the building.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Applied Mathematics

Theoretical and Mathematical Physics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

A surveyor stands $100 feet$ from a building and sights the top of the building at a $55 °$ angle of elevation. Find the height of the building.