A 50 m tree casts a shadow of 60 m . Find the sun's angle of elevation at that time.

If the angle is x, then

tan x = 50/60

To find the sun's angle of elevation, we can use the concept of similar triangles. The length of the shadow cast by the tree, the height of the tree, and the angle of elevation of the sun form a right triangle.

Let's assume the angle of elevation of the sun is θ.

Using the given information:
Length of the shadow = 60 m
Height of the tree = 50 m

In the right triangle, the opposite side is the height of the tree, and the adjacent side is the length of the shadow.

Using the trigonometric ratio tangent (tan):
tan(θ) = opposite/adjacent
tan(θ) = height of the tree/length of the shadow
tan(θ) = 50/60
tan(θ) = 5/6

Now, let's find the angle of elevation θ:
θ = tan^(-1)(5/6)
θ ≈ 39.81 degrees

Therefore, the sun's angle of elevation at that time is approximately 39.81 degrees.

To find the sun's angle of elevation, you can use the trigonometric function tangent. The angle of elevation is the angle between the horizontal ground and the line joining the top of the tree, the sun, and the bottom of the tree.

Let's use the given information to solve the problem step by step:

1. Draw a diagram: Sketch a triangle representing the situation. The tree represents the height, the shadow represents the base, and a line from the top of the tree to the end of the shadow represents the hypotenuse.

|
| \
| \
| \
|______\
50 m 60 m

2. Apply trigonometric tangent: In a right triangle, the tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the angle of elevation is the angle opposite the height of the tree.

tan(angle of elevation) = opposite/adjacent
tan(angle of elevation) = 50 m/60 m

3. Use a calculator to find the tangent of the angle of elevation: Divide 50 m by 60 m to get the decimal value.

tan(angle of elevation) = 0.8333

4. Find the angle of elevation: To find the angle itself, you can use the inverse tangent function (also known as arctan or tan^-1). This will give you the angle when you input the tangent value.

angle of elevation = arctan(0.8333)

Using a calculator, the angle of elevation is approximately 40.45 degrees.

Therefore, the sun's angle of elevation at that time is approximately 40.45 degrees.