91Ó°ÊÓ

In Exercises \(1-10,\) plot each complex number and find its absolute value. $$ z=4 i $$

In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$ B=85^{\circ}, C=15^{\circ}, b=40 $$

Solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$a=6, c=5, B=50^{\circ}$$

In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$ B=80^{\circ}, C=10^{\circ}, a=8 $$

Find the angle between \(\mathrm{v}\) and \(\mathrm{w}\). Round to the nearest tenth of a degree. $$ \mathbf{v}=6 \mathbf{i}, \quad \mathbf{w}=5 \mathbf{i}+4 \mathbf{j} $$

Use Heron's formula to find the area of each triangle. Round to the nearest square unit. \(a=5\) feet \(, b=5\) feet, \(c=4\) feet

Select the representations that do not change the location of the given point. $$\left(2,-\frac{3 \pi}{4}\right)$$ a. \(\left(2,-\frac{7 \pi}{4}\right)\) b. \(\left(2, \frac{5 \pi}{4}\right)\) c. \(\left(-2,-\frac{\pi}{4}\right)\) d. \(\left(-2,-\frac{7 \pi}{4}\right)\)

In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively. $$ a=9.3, b=41, A=18^{\circ} $$

The three given points are the vertices of \(a\) triangle. Solve each triangle, rounding lengths of sides to the nearest tenth and angle measures to the nearest degree. $$A(0,0), B(4,-3), C(1,-5)$$

A plane leaves airport \(A\) and travels 580 miles to airport \(B\) on a bearing of N34' E. The plane later leaves airport B and travels to airport \(\mathrm{C} 400\) miles away on a bearing of \(\mathrm{S} 74^{\circ} \mathrm{E}\) Find the distance from airport A to airport \(\mathrm{C}\) to the nearest tenth of a mile.