Question

A surveyor stands 150 feet from the base of a viaduct and measures the angle of elevation to be 46.2

∘
∘
. His eye level Is 6 feet above the ground. What is the height of the viaduct to the nearest foot?

Answer 1

Let's call the height of the viaduct "h".

Using trigonometry, we can set up the following equation:

tan(46.2) = h / (150 + 6)

Simplifying this equation, we get:

h = (150 + 6) * tan(46.2)

Solving this equation, we get:

h ≈ 148.5 feet

Rounding to the nearest foot, we get that the height of the viaduct is approximately 149 feet.