The angle of elevation to a nearby tree from a point on the ground is measured to be 66^{\circ} ∘ . How tall is the tree if the

Question

1 year ago

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point on the ground is 68 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.

1 answer:

Nimfa-mama [501] · Answer 1 · 2023-08-20T20:03:49+03:00

By comparing with a right triangle, we will see that the height of the tree is 62.12ft

We can compare the situation with a right triangle. Such that the hypotenuse measures 68 ft, and an angle measures 66°.

We want to get the height of the tree, which would be the opposite cathetus, then we can use the relation:

Sin(a) = (opposite cathetus)/hypotenuse.

Sin(66°) = H/68ft

Tan(66°)*68ft = H = 62.12ft

The height of the tree is 62.12ft

If you want to learn more about right triangles, you can read: