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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 tanθ, we can arrive at an function with the height h=x.tanθ-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 α and the measure of angle from A to TV tower is θ

03

Step 3. Find y

By using tangent function on the triangle ABC,

tanα=yxy=tanα

04

Step 4. Find h

Now consider the triangle ABD,

tanθ=h+yxh+y=xtanθh=xtanθ-y

which the height of the tower.

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Most popular questions from this chapter

the displacement d (in meters) of an object at time t (in seconds) is givend=6+2cos(2πt)

(a) Describe the motion of the object.

(b) What is the maximum displacement from its resting position?

(c) What is the time required for one oscillation?

(d) What is the frequency?

Solve each triangle.

a=10,b=8,c=5

Constructing a Highway U.S. 41, a highway whose primary directions are north–south, is being constructed along the west coast of Florida. Near Naples, a bay obstructs

the straight path of the road. Since the cost of a bridge is prohibitive, engineers decide to go around the bay. The illustration shows the path that they decide on and the measurements taken. What is the length of highway needed to go around the bay?

an object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume that the positive direction of the motion is up and the period is T (in seconds) under simple harmonic motion.

(a) Develop a model that relates the distance d of the object from its rest position after t seconds.

(b) Graph the equation found in part (a) for 5 oscillations using a graphing utility.

Given values:m=25,a=10,b=0.7,T=5

an object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up:

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