What is the angle of elevation of the sun when a tree 7.15m tall casts a shadow 10.1m long

clearly, if the angle is x,

tan(x) = 7.15/10.1

Let angle of elevation be x

Cosx =7.15/10.1
Cosx=0.7
X=cos-1(0.7)
X=45.5

To determine the angle of elevation of the sun, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.

In this case, the tree's height of 7.15m is the opposite side, and the shadow's length of 10.1m is the adjacent side. So, we can define the angle of elevation of the sun as:

tan(theta) = opposite side / adjacent side,
i.e., tan(theta) = 7.15m / 10.1m.

To find the angle itself (theta), we need to take the arctan (inverse tangent) of both sides of the equation:

theta = arctan(7.15m / 10.1m).

Using a scientific calculator or an online arctan calculator, you can input the value, and it will give you the angle in degrees.