Michael is constructing a boat ramp. He knows that the angle of elevation of the ramp is 25°. If the distance from the bottom of the boat ramp to the top of the boat ramp is 40 feet, what is the approximate height of the boat ramp?

The approximate height of the boat ramp is 18.6 ft

Step-by-step explanation:

This problem can be thought of as a right triangle

well to start we have to know the relationship between angles, legs and the hypotenuse in a right triangle

α = 25°

a: adjacent = 40ft

o: opposite = height

sin α = o/h

cos α = a/h

tan α = o/a

we see that it has (angle, adjacent, opposite)

we look at which meets those data between the sine, cosine and tangent

is the tangent

tan α = o/a

Now we replace the values and solve

tan 25° = o / 40ft

0.4662 * 40ft = o

18.65ft = o

The approximate height of the boat ramp is 18.6 ft