Mr M is sitting in a tree 50 meters above the ground. He spots two basketballs on the ground.
The angle of depression to the Nike ball is 48°, and the angle of depression to the adidas ball is 57°.
What is the horizontal distance between the balls, to the nearest meter?
To find the horizontal distance between the basketballs, we can use trigonometry and the information given.
Let's assume that Mr M is at point A in the tree, the Nike ball is at point B on the ground, and the Adidas ball is at point C on the ground.
We know that Mr M is 50 meters above the ground, so the height of triangle ABC is 50 meters. The angles of depression to the Nike and Adidas balls are 48° and 57° respectively, so we have the following diagram:
```
A
/|
50 / |
/ |
/ |
B/____|C
```
To find the horizontal distance between the balls, we need to find the length of side BC. To do this, we can use the tangent function:
tan(depression angle) = opposite / adjacent
For triangle ABC, the tangent of the angle of depression to the Nike ball is:
tan(48°) = BC / 50
Rearranging the equation, we can solve for BC:
BC = tan(48°) * 50
Similarly, the tangent of the angle of depression to the Adidas ball is:
tan(57°) = BC / 50
Solving for BC, we get:
BC = tan(57°) * 50
Using a calculator, we find that:
BC ≈ 58.62 meters
Therefore, the horizontal distance between the Nike ball and the Adidas ball, to the nearest meter, is 59 meters.