Chapter 8

The magnitudes of vectors \(\mathbf{A}\) and \(\mathbf{B}\) are given in the following table, as well as the angle between the vectors. For each, find the magnitude \(R\) of the resultant and the angle that resultant makes with vector \(\mathbf{B}\). $$\begin{array}{cc} & {\text { Magnitudes }} \\ \hline A & B & \text { Angle } \\ \hline 244 & 287 & 21.8^{\circ} \\ \hline \end{array}$$

Two stakes, \(A\) and \(B\), are \(88.6 \mathrm{m}\) apart. From a third stake \(C\), the angle \(A C B\) is \(85.4^{\circ},\) and from \(A,\) the angle \(B A C\) is \(74.3^{\circ} .\) Find the distance from \(C\) to each of the other stakes.

Find the reference angle for each given angle. $$163^{\circ}$$

The magnitudes of vectors \(\mathbf{A}\) and \(\mathbf{B}\) are given in the following table, as well as the angle between the vectors. For each, find the magnitude \(R\) of the resultant and the angle that resultant makes with vector \(\mathbf{B}\). $$\begin{array}{cc} & {\text { Magnitudes }} \\ \hline A & B & \text { Angle } \\ \hline 1.85 & 2.06 & 136^{\circ} \\ \hline \end{array}$$

Solve triangle \(A B C\). $$B=41.7^{\circ}, \quad a=199 \quad c=202$$

From a point on level ground, the angles of elevation of the top and the bottom of an antenna standing on top of a building are \(32.6^{\circ}\) and \(27.8^{\circ},\) respectively. If the building is \(125 \mathrm{ft}\) high, how tall is the antenna? Remember that angles of elevation or depression are always measured from the horizontal.

Find the reference angle for each given angle. $$274^{\circ}$$

The terminal side of an angle in standard position passes through the given point. Sketch the angle, compute the distance \(r\) from the origin to the point, and write the six trigonometric functions of the angle. Work to three significant digits. $$(-4.00,12.0)$$

The magnitudes of vectors \(\mathbf{A}\) and \(\mathbf{B}\) are given in the following table, as well as the angle between the vectors. For each, find the magnitude \(R\) of the resultant and the angle that resultant makes with vector \(\mathbf{B}\). $$\begin{array}{cc} & {\text { Magnitudes }} \\ \hline A & B & \text { Angle } \\ \hline 55.9 & 42.3 & 55.5^{\circ} \\ \hline \end{array}$$

Solve triangle \(A B C\). $$A=115^{\circ}, \quad b=46.8 \quad c=51.3$$

Find the reference angle for each given angle. $$305^{\circ}$$

The terminal side of an angle in standard position passes through the given point. Sketch the angle, compute the distance \(r\) from the origin to the point, and write the six trigonometric functions of the angle. Work to three significant digits. $$(24.0,-7.00)$$

The magnitudes of vectors \(\mathbf{A}\) and \(\mathbf{B}\) are given in the following table, as well as the angle between the vectors. For each, find the magnitude \(R\) of the resultant and the angle that resultant makes with vector \(\mathbf{B}\). $$\begin{array}{cc} & {\text { Magnitudes }} \\ \hline A & B & \text { Angle } \\ \hline 1.006 & 1.745 & 148.4^{\circ} \\ \hline \end{array}$$

Find the reference angle for each given angle. $$138.6^{\circ}$$

The terminal side of an angle in standard position passes through the given point. Sketch the angle, compute the distance \(r\) from the origin to the point, and write the six trigonometric functions of the angle. Work to three significant digits. $$(-15.0,-8.00)$$

The magnitudes of vectors \(\mathbf{A}\) and \(\mathbf{B}\) are given in the following table, as well as the angle between the vectors. For each, find the magnitude \(R\) of the resultant and the angle that resultant makes with vector \(\mathbf{B}\). $$\begin{array}{cc} & {\text { Magnitudes }} \\ \hline A & B & \text { Angle } \\ \hline 4483 & 5829 & 100.0^{\circ} \\ \hline \end{array}$$

Solve triangle \(A B C\). $$B=129^{\circ}, \quad a=186 \quad c=179$$

Solve triangle \(A B C\). $$A=44.47^{\circ}, \quad C=63.88^{\circ}, \quad c=1.065$$

Find the reference angle for each given angle. $$249.3^{\circ}$$

The terminal side of an angle in standard position passes through the given point. Sketch the angle, compute the distance \(r\) from the origin to the point, and write the six trigonometric functions of the angle. Work to three significant digits. $$(1.59,-3.11)$$

Solve triangle \(A B C\). $$A=158^{\circ}, \quad b=1.77 \quad c=1.99$$

The magnitudes of vectors \(\mathbf{A}\) and \(\mathbf{B}\) are given in the following table, as well as the angle between the vectors. For each, find the magnitude \(R\) of the resultant and the angle that resultant makes with vector \(\mathbf{B}\). $$\begin{array}{cc} & {\text { Magnitudes }} \\ \hline A & B & \text { Angle } \\ \hline 35.2 & 23.8 & 146^{\circ} \\ \hline \end{array}$$

If \(\theta\) is an angle in standard position, state in what quadrants its terminal side can lie if $$\theta=123^{\circ}.$$

The terminal side of an angle in standard position passes through the given point. Sketch the angle, compute the distance \(r\) from the origin to the point, and write the six trigonometric functions of the angle. Work to three significant digits. $$(-5.13,-1.17)$$

Find the resultant of each pair of vectors. $$4.83 \underline{/ 18.3^{\circ}} \text { and } 5.99 \underline{/ 83.5^{\circ}}$$

If \(\theta\) is an angle in standard position, state in what quadrants its terminal side can lie if $$\theta=272^{\circ}.$$

Trigonometric Functions of Any Angle by Calculator. Write, to four significant digits, the sine, cosine, and tangent of each angle. $$101^{\circ}$$

Solve triangle \(A B C\). $$a=11.3 \quad b=15.6 \quad c=12.8$$

Find the resultant of each pair of vectors. $$13.5 \underline{/ 29.3^{\circ}} \text { and } 27.8 \underline{/ 77.2^{\circ}}$$

Solve triangle \(A B C\). $$A=47.9^{\circ} \quad a=3.28 \quad c=2.35$$

If \(\theta\) is an angle in standard position, state in what quadrants its terminal side can lie if $$\theta=-47^{\circ}.$$

Trigonometric Functions of Any Angle by Calculator. Write, to four significant digits, the sine, cosine, and tangent of each angle. $$216^{\circ}$$

Solve triangle \(A B C\). $$a=1.475 \quad b=1.836 \quad c=2.017$$

Solve triangle \(A B C\). $$C=61.7^{\circ} \quad b=284 \quad c=382$$

If \(\theta\) is an angle in standard position, state in what quadrants its terminal side can lie if $$\theta=-216^{\circ}.$$

Trigonometric Functions of Any Angle by Calculator. Write, to four significant digits, the sine, cosine, and tangent of each angle. $$331^{\circ}$$

Find the resultant of each pair of vectors. $$83.2 \underline{/ 49.7^{\circ}} \text { and } 52.5 \underline{/ 66.3^{\circ}}$$

Solve triangle \(A B C\). $$a=369 \quad b=177 \quad c=199$$

Solve triangle \(A B C\). $$C=51.8^{\circ} \quad b=25.6 \quad c=24.9$$

A tower for a wind generator stands vertically on sloping ground whose inclination with the horizontal is \(11.6^{\circ} .\) From a point \(42.0 \mathrm{m}\) downhill from the tower (measured along the slope), the angle of elevation of the top of the tower is \(18.8^{\circ}\) How tall is the tower?

If \(\theta\) is an angle in standard position, state in what quadrants its terminal side can lie if $$\theta=415^{\circ}.$$

Trigonometric Functions of Any Angle by Calculator. Write, to four significant digits, the sine, cosine, and tangent of each angle. $$125.8^{\circ}$$

Find the resultant of each of the following sets of vectors. $$273 \underline{/ 34.0^{\circ}}, 179 \underline{/ 143^{\circ}}, 203 \underline{/ 225^{\circ}}, 138 \underline{/ 314^{\circ}}$$

Solve triangle \(A B C\). $$a=18.6 \quad b=32.9 \quad c=17.9$$

Solve triangle \(A B C\). $$A=45.6^{\circ} \quad a=7.83 \quad c=10.4$$

A vertical cellular phone antenna stands on a slope that makes an angle of \(8.70^{\circ}\) with the horizontal. From a point directly uphill from the antenna, the angle elevation of its top is \(61.0^{\circ} .\) From a point \(16.0 \mathrm{m}\) farther up the slope (measured along the slope), the angle of elevation of its top is \(38.0^{\circ} .\) How tall is the antenna?

If \(\theta\) is an angle in standard position, state in what quadrants its terminal side can lie if $$\theta=-415^{\circ}.$$

Trigonometric Functions of Any Angle by Calculator. Write, to four significant digits, the sine, cosine, and tangent of each angle. $$-62.85^{\circ}$$

Find the resultant of each of the following sets of vectors. $$72.5 \underline{/ 284^{\circ}}, 28.5 \underline{/ 331^{\circ}}, 88.2 \underline{/ 104^{\circ}}, 38.9 \underline{/ 146^{\circ}}$$

Solve triangle \(A B C\). $$a=5311 \quad b=6215 \quad c=7112$$