About 104 ft
To find out how tall the tree is, you can draw a diagram to help you picture it.
Picture the tree and you as a triangle. You are 55 ft from the tree. That means that the base of your triangle is 55 ft. The opposite side is the straight side you are trying to find. Let's say that value is x. Then, you have the angle of elevation from your eyes to the top of the tree, which is 61˚.
Tangent ratio = opposite side/adjacent side. These are the sides we have, so we are going to use them by using a tangent ratio.
So, now we have arrived at our equation: tan 61 = x/55
We can simplify this easily by multiplying 55 on both sides. x ÷ 55 = tan 61. x ÷ 55 • 55 = 55 • tan 61. So, x = 55 • tan 61 ≈ 99.2 ft
But, we still have to account for the height of your eyes. To do this, we just add 4.5 ft to 99.2 ft = 103.7 ≈ 104, so the tree is about 104 ft tall
