91Ó°ÊÓ

A guy wire reaches from the top of a pole to a stake in the ground. The stake is 10 feet from the foot of the pole. The wire makes an angle of \(65^{\circ}\) with the ground. Find, to the nearest foot, the length of the wire.

At a point on the ground 40 feet from the foot of a tree, the angle of elevation to the top of the tree is \(42^{\circ}\). Find the height of the tree to the nearest foot.

From the top of a lighthouse \(160 \mathrm{ft}\). above sea level, the angle of depression of a boat at sea is \(35^{\circ}\). Find, to the nearest foot, the distance from the boat to the foot of the lighthouse.

Given a triangle with sides of length \(\mathrm{a}, \mathrm{b}\), and \(\mathrm{c}\), show that \(\cos C=\left(a^{2}+b^{2}-c^{2}\right) / 2 a b\)