If the sun is 30 degrees up from the horizon and shining on a tree forming a 50 foot shadow, how tall is the tree?
We can use the tangent function to solve this problem. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
Let's assume the height of the tree is "h."
The tangent of the angle of elevation, 30 degrees, is the ratio of the height of the tree to the length of the shadow, 50 feet.
Therefore, tan(30) = h/50
Using a scientific calculator or referring to a tangent table, we find that tan(30) ≈ 0.5774.
Therefore, 0.5774 = h/50.
Solving for h, we have h = 0.5774 * 50.
So, the height of the tree is approximately 28.87 feet.