A 84-ft tree casts a shadow that is 130 ft long. What is the angle of elevation of the sun?
to find θ, note that
tanθ = 84/130
To determine the angle of elevation of the sun, we need to use the trigonometric concept of tangent. The tangent of an angle can be calculated by dividing the length of the side opposite the angle over the length of the side adjacent to the angle.
In this case, the height of the tree (opposite side) is 84 ft, and the length of the shadow (adjacent side) is 130 ft. Therefore, we can calculate the tangent of the angle by dividing 84 by 130:
tangent(angle) = opposite/adjacent
tangent(angle) = 84/130
Now, to find the angle itself, we need to take the inverse tangent (tan^-1) of the result:
angle = tan^-1(84/130)
Using a calculator, you can determine that angle is approximately 32.91 degrees. Therefore, the angle of elevation of the sun is approximately 32.91 degrees.