Question

A hawk sits on top of a tree and sees a mouse on the ground at an angle of depression of 25 degrees. The mouse is 25 km away from the base of the tree. Find the height of the tree.

Answer 1

To find the height of the tree, we can use trigonometry and the tangent function.

Step-by-step explanation:

To find the height of the tree, we can use trigonometry. The angle of depression of 25 degrees gives us a right triangle. The opposite side is the height of the tree and the adjacent side is the distance from the tree to the mouse. We can use the tangent function to find the height by dividing the opposite side by the adjacent side:

tan(25°) = Opposite side / 25 km

Rearranging the equation to solve for the height:

Opposite side = tan(25°) * 25 km

Now we can plug in the values and calculate the height:

Opposite side = tan(25°) * 25 km ≈ 0.466 * 25 km ≈ 11.65 km

Therefore, the height of the tree is approximately 11.65 km.