In triangle ABC, side a = 6, b = 8, and angle \$"C" = 60^\circ\$. Find the length of side (c) using the Law of Sines.

A) c = \$6\sqrt{3}\$

B) c = 9

C) c = \$4\sqrt{3}\$

D) c = 10

The triangle XYZ with side x = 5, side y = 7, and angle X = \$40^\circ\$, find all possible measures of angle Y using the Law of Sines.

A) \$"Y" = 50^\circ "and" "Y" = 90^\circ \$

B) \$"Y" = 40^\circ "and" "Y" = 140^\circ \$

C) \$"Y" = 70^\circ "and" "Y" = 80^\circ \$

D) \$"Y" = 30^\circ "and" "Y" = 140^\circ \$

Triangle DEF has side d = 10, side e = 12, and angle F = \$45^\circ\$. Find the angle (D) measure using the Law of Cosines and the Law of Sines.

A) D = \$30^\circ\$

B) D = \$60^\circ\$

C) D = \$75^\circ\$

D) D = \$45^\circ\$

An explorer travels 100 miles east, 200 miles north, and 250 miles on a bearing of \$330^\circ\$. Determine the explorer’s final position relative to the starting point using the Law of Sines and the Law of Cosines.

A) 150 miles, \$300^\circ\$

B) 350 miles, \$30^\circ\$

C) 350 miles, \$150^\circ\$

D) 375 miles, \$210^\circ\$

The quadrilateral PQRS with side lengths PQ = 8, QR = 10, RS = 6, PS = 9, and \$\angle "Q" = 100^\circ\$, find the measure of angle R using the Law of Cosines.

A) \$"R" = 70^\circ\$

B) \$"R" = 90^\circ\$

C) \$"R" = 120^\circ\$

D) \$"R" = 110^\circ\$

Given a triangle with angles A, B, and C and side lengths a, b, and c respectively, where angle A = 30°, angle B = 50°, and side b = 8 units. Find the length of side c using the Law of Sines.

A) \$ (12sqrt3)/3 \$

B) \$ (8sqrt3)/3 \$

C) \$ (16sqrt3)/3 \$

D) \$ (4sqrt3)/3 \$

From the top of a tower, the angle of depression to a car on the road is 60 degrees. If the tower is 40 meters high, how far is the car from the base of the tower?

A) \$ (20sqrt3)/3 \$ meters

B) \$ (40sqrt3)/3 \$ meters

C) \$ (10sqrt3)/3 \$ meters

D) \$ (30sqrt3)/3 \$ meters

In a triangle, the sides are in the ratio 3:4:5. If the smallest angle is 60 degrees, find the measures of the other two angles.

A) 80° and 100°

B) 60° and 80°

C) 40° and 60°

D) 20° and 10°

A flagpole casts a shadow that is 15 feet long when the angle of elevation of the sun is 45 degrees. If the flagpole is perpendicular to the ground, how tall is the flagpole?

A) 20 feet

B) 15 feet

C) 25 feet

D) 30 feet

A person measures the angles of a triangle as 30°, 60°, and 90°. Find the ratio of the lengths of the sides.

A) \$ 2:sqrt3​:2 \$

B) \$ 4:sqrt3​:2 \$

C) \$ 1:sqrt3​:2 \$

D) \$ 3:sqrt3​:2 \$