Question

Fill in the blank.

The light from a lamp casts a shadow of a man standing 10 feet away from
the lamppost. The shadow is 5 feet long. The angle of elevation from the tip
of the shadow to the lamp is 50°. To the nearest foot, the lamppost is _________
feet tall.

Answer 1

Answer: x ≈ 18 ft

Explanation:

We will use our trig knowledge to solve this.

The man is standing 10 ft away, but we also need to add the 5 ft shadow as well as that is a point on our triangle.

We can set up a simple trig equation of: tan(50) = x/15

x being the height of the lamppost.

Now we solve.

tan(50) = 1.1918

1.1918 *15 = x

x = 17.876

Now round to the nearest foot.

x ≈ 18 ft