A tree casts a 36 ft shadow. The angle of depression from the top of the tree to the tip of the shadow is 25°. Find the height of the tree to the nearest tenth.

make a sketch to see that

height/36 = tan 25°

height = 36tan25 = appr 16.8 ft

To find the height of the tree, we can use trigonometry and the concept of similar triangles.

Let's denote the height of the tree as "h".

From the given information, we know that the angle of depression from the top of the tree to the tip of the shadow is 25°. This means that we have a right triangle formed by the height of the tree, the length of the shadow, and the line connecting the top of the tree to the tip of the shadow.

Since we have a right triangle, we can use the trigonometric function tangent (tan) to relate the angle of depression to the height of the tree and the length of the shadow.

In trigonometry, tangent (tan) of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

So, we can write the equation as:

tan(25°) = h / 36 ft

To find the height of the tree (h), we can rearrange the equation:

h = tan(25°) * 36 ft

Now, we can calculate the height of the tree using a calculator:

h ≈ tan(25°) * 36 ft ≈ 15.9 ft

Therefore, the height of the tree is approximately 15.9 feet when rounded to the nearest tenth.