Question

A teacher standing on the stage is looking at his/her pupil who is standing on the ground. The height of the teacher and the pupil are 1.65 m and 1.5 m respectively. The angle of depression of the pupil from the teacher is 25° and the height of the stage is the same as the height of the pupil. Find the distance between the teacher and the pupil.

Answer 1

We can begin by drawing a diagram of the situation.

```
* Pupil
/|
/ |
/ | stage
/ |
/ |
/ |
/ |
/θ |
*--------* Teacher
```

From the diagram, we see that we have a right triangle with the teacher at the right angle, the distance between the teacher and the pupil as the hypotenuse, and the height difference between the teacher and the pupil as the opposite side. We can use the tangent function to relate the opposite and adjacent sides:

tan(25°) = opposite / adjacent

We want to solve for the adjacent side, which is the distance between the teacher and the pupil. Rearranging the equation, we get:

adjacent = opposite / tan(25°)

The opposite side is the height of the stage plus the height of the pupil:

opposite = 1.5 m + 1.5 m = 3 m

Substituting into the equation, we get:

adjacent = 3 m / tan(25°) ≈ 6.06 m

Therefore, the distance between the teacher and the pupil is approximately 6.06 meters.

Answer 2

Sure, I can help you with that. The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards at an object. It is used to measure the distance of the object from the ground or the observer.

In this problem, we can draw a right triangle ABC where A is the teacher, B is the pupil and C is the point on the ground below the teacher. The height of the stage is 1.5 m, so AC = 1.5 m + 1.5 m = 3 m. The angle of depression of the pupil from the teacher is 25°, so ∠BAC = 25°. We need to find BC, which is the distance between the teacher and the pupil.

Using trigonometry, we can write:

tan(25°) = AC/BC

BC = AC/tan(25°)

BC = 3/tan(25°)

BC ≈ 6.4 m

Therefore, the distance between the teacher and the pupil is about 6.4 m.