when the angle of elevation of the sun is 58 degrees. the shadow cast by a tree is 28 ft. long. how tall is the tree?
exact value of csc 450 degrees
To find the height of the tree, given the angle of elevation of the sun and the length of the shadow cast by the tree, we can use trigonometric ratios.
Let's denote the height of the tree as "h" and the angle of elevation of the sun as "θ." We are given that the angle of elevation is 58 degrees and the length of the shadow is 28 ft.
In a right triangle formed by the tree, its shadow, and the sun's rays, we have the following trigonometric ratio:
tangent (θ) = opposite / adjacent
In this case, the height of the tree "h" is the opposite side to the angle θ, and the length of the shadow "28" is the adjacent side. So, the equation becomes:
tan (θ) = h / 28
Now, we can plug in the given values and solve for "h." Let me calculate that for you.
Using a trigonometric calculator or table, we can find the value of tangent (58 degrees) ≈ 1.6019.
1.6019 = h / 28
To solve for "h," we can multiply both sides of the equation by 28:
28 * 1.6019 = h
h ≈ 44.85 ft
Therefore, the tree is approximately 44.85 feet tall.