Question

A surveyor standing 67 meters from the base of the building measures the angle to the top of the building and finds it to be 36 degrees. The surveyor then measures the angle to the top of the radio tower on the building and finds it is 46 degrees. How tall is the radio tower?

my choices are: a. 11.81m , b. 20.7 m, c. 7.66 m, d. 8.81 m
Any advice or assistance is appreciated. ...?

Answer 1

Option B is the correct answer.

Explanation:

Refer the the figure below of the question given.

The height of radio tower = CD

CD = AD - AC

We have

`tan46=(AD)/(AB)\\\\AD=ABtan46=67tan46\\\\tan36=(AC)/(AB)\\\\AC=ABtan36=67tan36\\\\CD=67tan46-67tan36=20.70m`

Option B is the correct answer.

Answer 2

Angle to the top of the building or base of the tower = 36 degrees
Angle to the top of the radio tower on the building = 46 degrees
Distance from the base at which the surveyor is standing = 67 meters
Let us assume the distance of the base of the tower from the surveyor = x1
Let us assume the distance of the top of the tower from the surveyor = x2
Then
tan(36) = x1/67
x1 = 67 tan(36)
and
tan(46) - x2/67
x2 = 67 tan(46)
Now
x2 - x1 = 67 tan(46) - 67 tan(36)
= 20.702
= 20.7 m
From the above deduction, it can be concluded that the correct option among all the options that are given in the question is the second option or option "b".