Question

The angle of depression from the top of a cliff to a boat sailing 100 m offshore is 32°. Calculate the height of the cliff, correct to the nearest metre.

Answer 1

A flagpole is 35 metres high. From a point A on the ground , the angle of elevation of the top of the flagpole is 30°.Find the distance from point A to the base of the flagpole to the nearest metre.

Answer 2

ABC is an isosceles triangle with AB =AC. What is the length of AC?

Height = 8, Base = 12

Answer 3

Review your basic trig functions.

Draw a diagram for each problem.
For the first, h/100 = tan 32°

Now try the others.

Answer 4

[AI-generated answer — Explain Bot]

To calculate the height of the cliff, we need to use trigonometry. Let's denote the height of the cliff as "h".

We have the angle of depression, which is the angle between the horizontal line from the top of the cliff to the boat and the downward line from the top of the cliff to the boat. In this case, the angle of depression is 32°.

We also know that the boat is sailing 100 m offshore. So, we can form a right triangle where the height of the cliff is the side opposite to the angle of depression, the distance offshore is the side adjacent to the angle of depression, and the hypotenuse of the triangle is the distance from the top of the cliff to the boat.

Using trigonometry, we can use the tangent function to find the height of the cliff:

tan(angle) = opposite/adjacent

tan(32°) = h/100

To isolate h, we can rearrange the equation:

h = tan(32°) * 100

Now we can calculate the height using a calculator:

h ≈ tan(32°) * 100

h ≈ 0.6249 * 100

h ≈ 62.49 m

Therefore, the height of the cliff is approximately 62.49 meters, rounded to the nearest meter.