From a boat on the lake, the angle of elevation to the top of a cliff is 26°35'. If the base of the cliff is 85 feet from the boat, how high is the cliff (to the nearest foot)?

A. 56 feet

B. 43 feet

C. 53 feet

D. 46 feet

I HAVE BEEN WORKING ON THIS FOREVER! please help me :( i don't know what i am doing wrong and none of my answers are any of these.

Thanks reiny, but you didn’t have to make the poster feel bad

Working forever?

takes about 30 seconds

make a sketch, let the height be h
tan 26° 35' = h/85
h = 85 tan 26.58333..° = 42.5339 ft
or according to the choices given, 43 feet

26° 35' = 26 + 35/60 = 26.583333..

To solve this problem, we can use trigonometry. The trigonometric function that relates the angle of elevation, the opposite side, and the adjacent side is the tangent (tan) function.

Given that the angle of elevation to the top of the cliff is 26°35' and the base of the cliff is 85 feet from the boat, we can set up the following equation:

tan(angle of elevation) = height of cliff / distance to the cliff

Let's convert the angle of elevation to decimal degrees:

26°35' = 26 + 35/60 ≈ 26.58333°

Now we can substitute the values into the equation:

tan(26.58333°) = height of cliff / 85 feet

Next, solve for the height of the cliff:

height of cliff = tan(26.58333°) * 85 feet

Using a calculator:

height of cliff ≈ 46 feet (rounded to the nearest foot)

Therefore, the height of the cliff is approximately 46 feet.

The correct answer is D. 46 feet.

To find the height of the cliff, we can use trigonometry. In this case, we can use the tangent function since we have the angle of elevation and the distance from the boat to the base of the cliff.

Here's how to solve it step-by-step:

1. Convert the angle from degrees and minutes to decimal form. We have 26°35', which is equivalent to 26 + 35/60 = 26.5833°.

2. Next, convert the angle from degrees to radians by multiplying it by π/180. So, 26.5833° * π/180 ≈ 0.4645 radians.

3. Use the tangent function to find the height of the cliff. The tangent of the angle of elevation is equal to the height of the cliff divided by the distance from the boat to the base of the cliff.

tan(0.4645) = height / 85

4. Rearrange the equation to solve for the height:

height = tan(0.4645) * 85

5. Use a calculator to find the value of tan(0.4645), which is approximately 0.5095.

height = 0.5095 * 85

6. Multiply 0.5095 by 85 to get the height:

height ≈ 43.34 feet

Since we are asked to round to the nearest foot, the height of the cliff is approximately 43 feet. Therefore, the correct answer is B. 43 feet.