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 ...?

Question

Giovani Riggs

Mathematics

5 April, 06:07

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 ...?

+5

Answers (1)

Know the Answer?

Scarlet Knapp · Answer 1

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".