Question

2. The angle of elevation of the top of a vertical

cliff, as seen from a boat 120 m away, is 32°.
The angle of elevation of the top of a flagpole
at the edge of the cliff, as seen from the boat,
is 37º. Find the height of the flagpole.
​

Answer 1

To find the height of the flagpole, use the tangent function with the angles of elevation of the top of the cliff and the flagpole. Solving for the respective heights, the height of the cliff is 73.16 m and the height of the flagpole is 97.85 m.

Step-by-step explanation:

To find the height of the flagpole, we can use trigonometry. We can create a right triangle with the boat as the base, the distance from the boat to the top of the cliff as the adjacent side, and the height of the flagpole as the opposite side. Using the angle of elevation of the top of the cliff, we can find the height of the cliff using the tangent function: tan(32°) = height of the cliff / 120. Solving for the height of the cliff, we get 120 * tan(32°) = 73.16 m.

Next, we can use the angle of elevation of the flagpole to find the height of the flagpole. We can use the same right triangle from before, but now the distance from the boat to the top of the flagpole is the adjacent side. Using the angle of elevation of the flagpole, we can find the height of the flagpole using the tangent function: tan(37°) = height of the flagpole / 120. Solving for the height of the flagpole, we get 120 * tan(37°) = 97.85 m.

Answer 2

Answer: 15.44 m

Step-by-step explanation:

We can think this as two triangle rectangles.

In both cases, the adjacent cathetus is 120m.

When the angle is 32°, the opposite cathetus will be the height of the cliff.

When the angle is 37°, the opposite cathetus will be the heigth of the cliff plus the height of the flagpole.

Then we need to compute both of them and calculate the difference.

We can use the trigonometric relation:

Tan(θ) = (opposite cathetus)/(adjacent cathetus)

in this case we have:

Tan(32°) = (height of the cliff)/(120m)

Tan(32°)*120m = height of the cliff = 74.98m

Now we can use the other angle to compute:

Tan(37°) = (heigth of the cliff + heigth of the flagpole)/120m

Tan(37°)*120m = heigth of the cliff + heigth of the flagpole = 90.42m

Then the height of the flagpole will be:

H = 90.42m - 74.98m = 15.44 m