From a boat on the lake, the angle of elevation to the top of a cliff is 24 degrees 19'. If the base of the cliff is 2994 feet from the boat, how high is the cliff (to the nearest foot) ?

1353 ft

Step-by-step explanation:

The cliff height and the distance from its base to the boat form the legs of a right triangle. The cliff height is the leg opposite the elevation angle, and the distance to the boat is the leg adjacent. Given these two legs of the triangle, the tangent relation seems useful:

Tan = Opposite/Adjacent

We want to find the cliff height (opposite), so we can multiply this equation by Adjacent:

Opposite = Adjacent*Tan

cliff height = (2994 ft) (tan (24°19')) ≈ 1353 ft

The cliff is about 1353 feet high.