this is a trig question?

Question

An observer notices that the angle of elevation of the top of a neighboring building is 60 degrees. if the distance from the observer to the neighboring building is 40 ft how tall is the building.

is the answer 40square root 3?

Answer 1

Don't forget SOH CAH TOA (pronounced "so caw toe-ahh"), which means:
Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Tan = Opposite / Adjacent

I always recommend to my students that they draw/sketch the situation. So draw a picture and double check my math, but I believe that the appropriate equation here is:

Tan 60 = x/40

Rearrange and solve for x before evaluating Tan 60.

40(Tan 60)= x
69.28 is approximately equal to x

The exact value for tan 60 is sq. root of 3. So, your answer is mathematically correct. My question is how many people would say "My building? Oh, it's 40 sq. root 3 feet tall." You may want to ask if the importance in this exercise is finding the exact answer or finding the most applicable answer.

Hope this helps.

Answer 2

Sketch a triangle ABC
AB is vertical and B is at ground level
AB = h ft
C is at ground level
Angle ABC is right angle
Angle ACB = 60°
tan 60° = h / 40
h = 40 x tan 60°
h = 40.√3 ft

Answer 3

You got it right!