Exam 13: Right Triangle Trigonometry

In ac (alternating current) circuits, the relationship between the impedance Z (in ohms), the resistance R (in ohms), the phase angle $\theta$ , and the reactance X (in ohms) is shown by the right triangle in the illustration. a. Find the impedance if the resistance is 380 ? and the phase angle is 23 ^o. Round your answer to the appropriate number of significant digits. b. Suppose the resistance is 520 ? and the impedance is $7 \overline { 0 } 0$ ? . What is the phase angle? Round your answer to the appropriate number of significant digits. c. Suppose the reactance is 190 ? and the resistance is 220 ? . Find the impedance and the phase angle. Round your answers to the appropriate number of significant digits.

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 0.6211 cm, c = 0.7937 cm

Using the illustration, find the measure of each acute angle for the right triangle below and express your answer using the appropriate rule for significant digits. $a = 25.58$ ft, $c = 40.0 1$ ft A = __________°   B = __________°

Find the unknown sides of the right triangle (see illustration). Round your answer to the appropriate number of significant digits. $c = 185.2 \mathrm {~cm} , \angle B = 61.47 ^ { \circ }$

Use the triangle in the illustration. Find cos K rounded to three significant digits.

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. b = 1,227 ft, c = 1,378 ft

Using the illustration, solve the right triangle. Express your answer using the appropriate number of significant digits. $\angle A = 52.5 ^ { \circ } , a = 76.0 \mathrm {~mm}$ b =  __________ mm c =  __________ mm ∠B =  __________ $^ { \circ }$

Find the angle rounded to the nearest hundredth of a degree. sin A = 0.9382

The angle adjacent to side e is _____.

Twelve equally spaced holes must be drilled on a 13.700-in.-diameter bolt circle. (See the illustration.) What is the straight-line center-to-center distance between two adjacent holes? Round your answer to the appropriate number of significant digits.

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 15.2 m, c = 84.3 m

Solve the right triangle. Round your answer to the appropriate number of significant digits. $b = 264.5 \mathrm {~m} , c = 390.5 \mathrm {~m}$

Find the angle rounded to the nearest tenth of a degree. tan C = 0.8660

Solve the right triangle. Round your answer to the appropriate number of significant digits. $a = 46.78 \mathrm {~m} , b = 19.34 \mathrm {~m}$

Find the unknown sides of the right triangle (see illustration). Express your answer using the appropriate number of significant digits. $c = 289.4 \mathrm {~cm} , \angle A = 24.61 ^ { \circ }$ a = __________ cm b = __________ cm

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 45.8 cm, c = 58.5 cm

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 35.1 mm, b = 60.7 mm, c = 70.2 mm

Solve the right triangle. Round your answer to the appropriate number of significant digits. $a = 13.5 \mathrm {~cm} , b = 13.5 \mathrm {~cm}$

Find the value of the trigonometric ratio rounded to four significant digits. sin 48.3° = __________

Solve the right triangle. Round your answer to the appropriate number of significant digits. $\angle B = 22.9 ^ { \circ } , c = 56.0 \mathrm { mi }$