Question

From a boat on the lake, the angle of elevation to the top of a cliff is 25°24'. If the base of the cliff is 1183 feet from the boat, how high is the cliff (to the nearest foot)?

A. 509 feet
B. 850 feet
C. 454 feet
D. 631 feet

Answer 1

To find the height of a cliff using the angle of elevation and horizontal distance, use the tangent function and multiply by the distance to calculate the height, rounding to the nearest foot.

Step-by-step explanation:

The student is asking to find the height of a cliff given the angle of elevation and the horizontal distance from the base. To solve this, we can use the tangent function in trigonometry because the tangent of an angle in a right-angled triangle is the ratio of the opposite side (the height of the cliff) to the adjacent side (the horizontal distance to the base).

Here is how to calculate it step by step:

1. Convert the angle to decimal form: 25°24' is equal to 25.4°.
2. Use the tangent function: tan(25.4°) = height / 1183 feet.
3. Multiply both sides by the horizontal distance to find the height: height = tan(25.4°) × 1183 feet.
4. Use a calculator to find the tangent of 25.4°, then multiply by 1183.
5. Round the answer to the nearest foot.

Following these steps, the calculated height of the cliff, rounded to the nearest foot, can be determined to select the correct answer among the given options.