91Ó°ÊÓ

You are on a fishing boat that leaves its pier and heads east. After traveling for 25 miles, there is a report warning of rough seas directly south. The captain turns the boat and follows a bearing of \(\mathrm{S} 40^{\circ} \mathrm{W}\) for 13.5 miles. a. At this time, how far are you from the boat's pier? Round to the nearest tenth of a mile. b. What bearing could the boat have originally taken to arrive at this spot?

In Exercises 45–46, find the area of the triangle with the given vertices. Round to the nearest square unit. $$ (-3,-2),(2,-2),(1,2) $$

Two fire-lookout stations are 10 miles apart, with station \(\mathrm{B}\) directly east of station A. Both stations spot a fire. The bearing of the fire from station \(A\) is \(N 25^{\circ} \mathrm{E}\) and the bearing of the fire from station \(\mathrm{B}\) is \(\mathrm{N} 56^{\circ} \mathrm{W}\). How far, to the nearest tenth of a mile, is the fire from each lookout station?

Explaining the Concepts What is a polar equation?

Convert each rectangular equation to a polar equation that expresses r in terms of \(\theta\). $$ x+5 y=8 $$

A pine tree growing on a hillside makes a \(75^{\circ}\) angle with the hill. From a point 80 feet up the hill, the angle of elevation to the top of the tree is \(62^{\circ}\) and the angle of depression to the bottom is \(23^{\circ} .\) Find, to the nearest tenth of a foot, the height of the tree.

Why can't the Law of Sines be used in the first step to solve an SAS triangle?

A pier forms an \(85^{\circ}\) angle with a straight shore. At a distance of 100 feet from the pier, the line of sight to the tip forms a \(37^{\circ}\) angle. Find the length of the pier to the nearest tenth of a foot.

Describe a strategy for solving an SSS triangle.

After a wind storm, you notice that your 16 -foot flagpole may be leaning, but you are not sure. From a point on the ground 15 feet from the base of the flagpole, you find that the angle of elevation to the top is \(48^{\circ} .\) Is the flagpole leaning? If so, find the acute angle, to the nearest degree, that the flagpole makes with the ground.