Chapter 4

Solve each triangle. $$a=4, c=3, \beta=100^{\circ}$$

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$(3,6)$$

Find \((a)\) the complement and \((b)\) the supplement of the given angles. $$18^{\circ}$$

Solve each triangle. $$a=6, b=10, \gamma=80^{\circ}$$

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$.(8,4)$$

Find \((a)\) the complement and \((b)\) the supplement of the given angles. $$39^{\circ}$$

Solve each triangle. $$b=7, c=2, \alpha=16^{\circ}$$

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$\left(\frac{1}{2}, \frac{2}{5}\right)$$

Find \((a)\) the complement and \((b)\) the supplement of the given angles. $$42^{\circ}$$

Solve each triangle. $$b=5, a=6, \gamma=170^{\circ}$$

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$\left(\frac{4}{7}, \frac{2}{3}\right)$$

Find \((a)\) the complement and \((b)\) the supplement of the given angles. $$57^{\circ}$$

Solve each triangle. $$b=5, c=5, \alpha=20^{\circ}$$

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$(-2,4)$$

Find \((a)\) the complement and \((b)\) the supplement of the given angles. $$89^{\circ}$$

Solve each triangle. $$a=4.2, b=7.3, \gamma=25^{\circ}$$

Classify triangle problem as cases AAS, ASA, SAS, SSA, or SSS on the basis of the given information. (Check your book to see figure) $$\beta, \gamma, \text { and } a$$

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$(-1,3)$$

Find \((a)\) the complement and \((b)\) the supplement of the given angles. $$75^{\circ}$$

Solve the following triangles with the given measures. $$\alpha=45^{\circ}, \beta=60^{\circ}, a=10 \mathrm{m}$$

Solve each triangle. $$a=9, c=12, \beta=23^{\circ}$$

Find the measure (in radians) of a central angle \(\theta\) that intercepts an are of length \(s\) on a circle with radius \(r\). \(r=22\) in., \(s=4\) in.

Solve each triangle. $$b=6, c=13, \alpha=16^{\circ}$$

Solve the following triangles with the given measures. $$\beta=75^{\circ}, \gamma=60^{\circ}, b=25 \text { in. }$$

Find the measure (in radians) of a central angle \(\theta\) that intercepts an are of length \(s\) on a circle with radius \(r\). \(r=6\) in., \(s=1\) in.

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$(-9,-5)$$

Solve each triangle. $$a=4, c=8, \beta=60^{\circ}$$

Solve the following triangles with the given measures. $$\alpha=46^{\circ}, \gamma=72^{\circ}, b=200 \mathrm{cm}$$

Find the measure (in radians) of a central angle \(\theta\) that intercepts an are of length \(s\) on a circle with radius \(r\). \(r=100 \mathrm{cm}, s=20 \mathrm{mm}\)

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$(-\sqrt{2}, \sqrt{3})$$

Solve each triangle. $$b=3, c=\sqrt{18}, \alpha=45^{\circ}$$

Solve the following triangles with the given measures. $$\gamma=100^{\circ}, \beta=40^{\circ}, a=16 \mathrm{ft}$$

Find the measure (in radians) of a central angle \(\theta\) that intercepts an are of length \(s\) on a circle with radius \(r\). \(r=1 \mathrm{m}, s=2 \mathrm{cm}\)

Find the measure (in radians) of a central angle \(\theta\) that intercepts an are of length \(s\) on a circle with radius \(r\). \(r=\frac{1}{4}\) in., \(s=\frac{1}{32}\) in.

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$(-\sqrt{5},-\sqrt{3})$$

Solve the following triangles with the given measures. $$\beta=104.2^{\circ}, \gamma=33.6^{\circ}, a=26 \mathrm{in}$$

Find the measure (in radians) of a central angle \(\theta\) that intercepts an are of length \(s\) on a circle with radius \(r\). \(r=\frac{3}{4} \mathrm{cm}, s=\frac{3}{14} \mathrm{cm}\)

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$(-\sqrt{6},-\sqrt{5})$$

Solve each triangle. $$a=4, b=4, c=5$$

Convert from degrees to radians. Leave the answers in terms of \(\pi\). $$30^{\circ}$$

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$\left(-\frac{10}{3},-\frac{4}{3}\right)$$

Solve the following triangles with the given measures. $$\alpha=45^{\circ}, \gamma=75^{\circ}, c=9 \text { in }$$

The terminal side of an angle \(\theta\) in standard position passes through values of the six trigonometric functions for angle \(\theta\) $$\left(-\frac{2}{9},-\frac{1}{3}\right)$$

Convert from degrees to radians. Leave the answers in terms of \(\pi\). $$60^{\circ}$$

Match the trigonometric function values. a. \(\frac{1}{2}\) b. \(\frac{\sqrt{3}}{2}\) c. \(\frac{\sqrt{2}}{2}\) $$\sin 60^{\circ}$$

Solve the following triangles with the given measures. $$\beta=26^{\circ}, \gamma=57^{\circ}, c=100 \mathrm{yd}$$

Indicate the quadrant in which the terminal side of \(\theta\) must lie in order for the information to be true. \(\cos \theta\) is positive and \(\sin \theta\) is negative.

Match the trigonometric function values. a. \(\frac{1}{2}\) b. \(\frac{\sqrt{3}}{2}\) c. \(\frac{\sqrt{2}}{2}\) $$\cos \left(\frac{\pi}{6}\right)$$

Convert from degrees to radians. Leave the answers in terms of \(\pi\). $$45^{\circ}$$

Solve each triangle. $$a=1492, b=2001, c=1776$$