Geometry Trig applications Problem

Question

An antenna is atop the roof of a 100-foot building, 10 feet from the edge, as shown in the figure below. From a point, 50 feet from the base of the building, the angle from ground level to the top of the antenna is 660. Find x, the length of the antenna,

Answer 1

To solve this problem remember the acronym SOHCAHTOA:

Sin theta= opp

___

hyp

Cos theta= Adj

____

hyp

Tan theta: Opp

____

Adj

This problem gives you the angle measurement.

This problem tells you to use tangent.

Tan theta= opp

___

adj

tan(66)= 100+x

_____

50+10

tan(66)=100+x

_____

60

60*tan(66)=100+x

134.8=100+x

When you find what the result of tan is you subtract the value from 100.

134.8=100+x

-100 -100

______________

34.8=x

The solution to this problem should turn out to be 34.8

ANS: 34.8

Answer 2

In solving problems like this, always try to find the relevant right triangle. In this case, the vertices are at the observer's location of the ground, the top of the antenna, and the spot on the ground directly below the antenna. Fill in the known distances and angles. To solve this, you'll use the tangent function:

tan(θ) = opposite/adjacent

tan(66°) = height of antenna from ground / distance of observer to spot on ground directly below antenna

Let x = the length of the antenna. The height of the tower above the ground is 100 feet (building height) + x.

tan(66°) =(100 + x) / (50 + 10)

tan(66°) =(100 + x) / (60)

60·tan(66°) = 100 + x

Solve for x, the length of the antenna. Use you calculator to compute the tangent value.