Question

From the top of a cliff 90m high the angle of depression of a boat on the sea is 26.2degrees. calculate how far the boat is from the foot of the cliff

Answer 1

189.36 metres

Explanation:

We can use trigonometry to solve this problem.

Let's draw a diagram to help visualize the situation:

```

|

|

|90m

|

|

|

-----------|--------------------

x

```

We can see that the angle of depression is the angle formed by a horizontal line from the top of the cliff to the boat, and a line of sight from the top of the cliff to the boat. We can also see that the height of the cliff is 90 meters.

Using trigonometry, we can find the distance x between the boat and the foot of the cliff:

tan(26.2°) = opposite / adjacent

tan(26.2°) = 90 / x

To solve for x, we can rearrange the equation:

x = 90 / tan(26.2°)

x ≈ 189.36 meters

Therefore, the boat is approximately 189.36 meters from the foot of the cliff.