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Audio 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?
Wiki User
∙ 11y ago
64.9408 ft.
You calculate this using trigonometry. Sine, cosine, and tangent are fractions made by dividing the length of one of the sides of a triangle by one of the other sides. The sine, cosine, or tangent for an angle is always the same, so if we know the angle and the length of one of the sides we can calculate the lengths of the other sides. Assuming the tree is at 90o to the ground we have a right angled triangle. The side of the triangle from john to the top of the tree is the hypotenuse ( the longest side) from John to the base of the tree is the adjacent side, and the ground to the top of the tree is the opposite side. Because we know the length of the adjacent side and need to find the length of the opposite, the function we use is the tangent, tangent = length of opposite side divided length of adjacent side.
The angle is 33o so we look up tan 33o which is 0.6494.
Tan(33)= length of opposite/length of adjacent
(move length adj by multiplying both sides by length adj)
Tan(33) x length of adjacent = length of opposite
(length from John to tree 100ft= 30.84 metres)
0.6494 x 30.48 metres = length of opposite (which is the height of the tree)
Tree height = 19.79 metres (or 64 feet 11 and 9/64 inches)
Wiki User
∙ 11y ago
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