An oak tree is splintered by lightning 260 cm up its trunk, so that the top part of the tree touches the ground. The angle the top of the standing tree forms with the ground is 74 degrees.
How tall was the tree to the nearest tenth of a metre, before it was splintered?

Question

Vocaloid · Answer

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here's a quick sketch of the situation. the left side is the part of the tree that is still vertical. the top vertex of this triangle is the point where the tree splintered. the hypotenuse is the rest of the tree. I've labelled that part as x. The angle between the top of the tree, and the ground, is 74 degrees.

from the perspective of the 74 degree angle, we have the opposite side (260 cm) and we want to know the hypotenuse. use sin(theta) = opposite/hypotenuse. solve for the hypotenuse, x. then add x + 260 to get the full height of the tree.