John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33º . How tall is the tree?

The tree is 64.9 ft tall.

Step-by-step explanation:

Think of a right triangle. Draw the right triangle. The tree is a vertical side of the triangle, so it is a leg with unknown length, so call its length y. The ground, is a horizontal leg with length 100 ft. The angle from endpoint of the horizontal leg on the ground away from the tree to the top of the tree is 33º.

For the 33º angle, y is the opposite leg, and 100 ft is the adjacent leg.

The trig ratio that relates the lengths of the opposite leg to the adjacent leg is the tangent.

tan A = opp/adj

tan 33º = y/100

y = 100 * tan 33º

y = 64.9

The tree is 64.9 ft tall.

x

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