Question

From a point on the ground , the angle of elevation to the top of a 60 foot radio antenna sitting atop a hill is 39 degrees. The angle of elevation to the top of the hill from the same point on the ground is 36 degrees. How high is the hill?

Answer 1

Answer:

523.69 ft

Step-by-step explanation:

consider the diagram in the image : x is the height of the hill. 600 foot is the antenna.  

there are two triangles ABC and ABE

since they have nothing in common except AB ( the ground), i built two equations basing this.

for triangle ABC :  Tan 39 = (x + 60) / a

for triangle ABE : Tan 36 = x / a

solve for 'a'  in both the equations, you get:

a = (x +60) / tan 39

a = x/ tan 36

now you can equate both the equations

(x + 60) / tan 39 = x/ tan 36

(tan 36)x + (tan 36)60 = (tan 39)x

solve for x .....

x = 523.6876....