A spotlight is set up on the ground with an angle of 70°. The light is 240 inches from the building. At what height does the spotlight hit the building?

Question

intergrated math high school math

Answer 1

I am assuming 240 inches is the ground distance from the spotlight to the building, and the light is shining on the top of the building.

 

You have a right triangle, with a vertical leg equal to the height of the building (h), and a horizontal base (b) of 240 inches.

 

Then

 

tan(70º) = h/b

 

h = b*tan(70º) = (240 inches) * tan (70º) ≅ 659 inches 

Answer 2

Cynthia, we can use the law of sines with what is given and what we can infer.

 

We have an unkown side length opposite the 70 degree angle. We can assume that the angle between the ground and the building is 90 degrees, so the angle between the building and beam of light (opposite the ground) is 20 degrees.

 

sin20/240 = sin70/x

xsin20 = 240sin70

x = 240sin70/sin20

 

I don't have a calculator handy, but plug it in to yours for your answer!