A tree stands 75feet tall and cast a shadow that is 50feet long. What is the angle of elevation from where the shadow ends and the top of the tree
tan Θ= opposite/ adjacent
= height of the tree/ shadow length
= 75/50
=1.5
Θ = tan ^-1(1.5)
Θ = 56°
To find the angle of elevation, we can use the inverse tangent function since we have the opposite and adjacent sides of a right triangle.
The opposite side is the height of the tree (75 feet), and the adjacent side is the length of the shadow (50 feet).
We can use the formula
tan(theta) = opposite/adjacent,
where theta represents the angle of elevation. Rearranging the formula, we have
theta = arctan(opposite/adjacent).
Plugging in the values, we get
theta = arctan(75/50).
Now, let's calculate the angle of elevation:
theta = arctan(75/50)
Using a calculator,
theta ≈ 56.31 degrees.
Hence, the angle of elevation from where the shadow ends to the top of the tree is approximately 56.31 degrees.