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Chapter 8: Q. 82 (page 520)

Explain how you would measure the height of a TV tower that is on the roof of a tall building.

Short Answer

Expert verified

By using the trigonometric function tan胃, we can arrive at an function with the height h=x.tan胃-y

Step by step solution

01

Step 1. Given Information

The TV tower is on the roof of the building.

02

Step 2. Construction of TV tower on the building.

Let BCbe the height of the building and CDbe the height of the TV tower on the building.

Let Abe the point which is xfeet away from the building so that AB=x.

Let the measure of an angle from A to C be 伪 and the measure of angle from A to TV tower is 胃

03

Step 3. Find y

By using tangent function on the triangle ABC,

tan伪=yxy=tan伪

04

Step 4. Find h

Now consider the triangle ABD,

tan胃=h+yxh+y=xtan胃h=xtan胃-y

which the height of the tower.

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