91Ó°ÊÓ

A distress signal from a ship, \(S,\) is received by two coast guard stations located 3.8 miles apart along a straight coastline. From station \(A,\) the signal makes an angle of \(48^{\circ}\) with the coastline and from station \(B\) the signal makes an angle of \(67^{\circ}\) with the coastline. Find, to the nearest tenth of a mile, the distance from the ship to the nearer station.

Let \(A B C D\) be a parallelogram with \(A B=c, B C=a,\) and \(\mathrm{m} \angle B=\theta .\) a. Write a formula for the area of parallelogram \(A B C D\) in terms of \(c, a,\) and \(\theta\) . b. For what value of \(\theta\) does parallelogram \(A B C D\) have the greatest area?

Use the formula cos \(C=\frac{a^{2}+b^{2}-c^{2}}{2 a b}\) to show that the measure of each angle of an equilateral triangle is \(60^{\circ} .\)

From a point 50 feet from the foot of a vertical monument, the measure of the angle of elevation of the top of the monument is 65 degrees. What is the height of the monument to the nearest foot?