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.
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?
1 answer