The sun is 21 ∘ above the horizon. It makes a 45 m -long shadow of a tall tree.

Question

Please reply with answer only!

Answer 1

I'll assume you are looking for how tall the tree is.

Step 1: Construct the right triangle with the known variables. You know one of the vertical leg represents the height of the tree and the horizontal leg represents the 45m shadow. As well, you know the angle between the horizontal leg and the hypothenuse is 21-degrees, as that is the angle the sun is casting on the tree.

Step 2: Use trigonometry to solve for the height of the tree. A simple one to use in this case is tan(θ) since tan(θ) = opposite/adjacent. The "opposite" in this case is the vertical leg or the height of the tree we are looking for. Let's label this "x". The "adjacent" is the 45m shadow the tree casts. The θ is the 21-degrees from the sun.

tan(21 degrees) = x/45

x = 17.27m