91Ó°ÊÓ

You are on a fishing boat that leaves its pier and heads east. After traveling for 30 miles, there is a report warning of rough seas directly south. The captain turns the boat and follows a bearing of \(\mathrm{S} 45^{\circ} \mathrm{W}\) for 12 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?

The rectangular coordinates of a point are given. Find polar coordinates of each point. Express \(\theta\) in radians. $$(0,-6)$$

Find the quotient \(\frac{z_{1}}{z_{2}}\) of the complex numbers. Leave answers in polar form. In Exercises \(49-50\), express the argument as an angle between \(0^{\circ}\) and \(360^{\circ}\). $$\begin{array}{l} z_{1}=\cos 80^{\circ}+i \sin 80^{\circ} \\ z_{2}=\cos 200^{\circ}+i \sin 200^{\circ} \end{array}$$

A Major League baseball diamond has four bases forming a square whose sides measure 90 feet each. The pitcher's mound is 60.5 feet from home plate on a line joining home plate and second base. Find the distance from the pitcher's mound to first base. Round to the nearest tenth of a foot.

Convert each rectangular equation to a polar equation that expresses \(r\) in terms of \(\theta\) $$x=7$$

Find the work done in pushing a car along a level road from point \(A\) to point \(B, 80\) feet from \(A,\) while exerting a constant force of 95 pounds. Round to the nearest foot-pound.

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

Describe a strategy for solving an SAS triangle.

Describe a strategy for solving an SSS triangle.

Under what conditions would you use Heron's formula to find the area of a triangle?