Rodney stood 30 m away from the light house in such a way that the angle of elevation of the top of the light house from his eyes was 45º.

Rodney"s height is  1.4 m. Find the height of the light house.

Asked by Topperlearning User | 2nd Nov, 2017, 09:36: AM

Expert Answer:

Here, AB is the light house and CD is the observer, Rodney.
The angle of elevation is represented by angleADE.
Hence, we can see that in this case, ADE is a triangle, right angled at E and we are required to find out the height of the light house.
We have       AB = AE + BE
                     AB = AE + 1.4
And              DE = CB = 30 m
Now, to determine AE, we choose a trigonometric ratio that involves both AE and DE.
Let us choose the tangent of the angle of elevation.
So, the height of the light house (AB) = (30 + 1.4) m = 31.4 m

Answered by  | 2nd Nov, 2017, 11:36: AM