A triangle has an angle of 45 degrees, and its opposite side is 10 units. Another angle is 60 degrees. What is the length of the side opposite the 60-degree angle?

A) \$ 5\sqrt6 \$

B) \$ 2\sqrt3 \$

C) \$ 3\sqrt2 \$

D) \$ 5\sqrt3 \$

If A = \$ \sqrt5\$, B = x, C = 5, and c = 135°. Find the value of x.

A) \$\sqrt2\$

B) \$ \sqrt10\$

C) \$ 2\sqrt5\$

D) \$5 \sqrt2\$

Given a triangle where \$A = 40^\circ\$, \$B = 60^\circ\$, and c = 8 units. Find the lengths of the remaining sides and the other angles.

A) \$C = 70^\circ\$, a = 4.214 units, and b = 7.052 units

B) \$C = 120^\circ\$, a = 3.12 units, and b = 7.532 units

C) \$C = 80^\circ\$, a = 5.214 units, and b = 7.052 units

D) \$C = 60^\circ\$, a = 5.214 units, and b = 6.122 units

In triangle GHI, angle G = 35 degrees, angle H = 65 degrees, and side h (opposite angle H) is 14 units. Find side g (opposite angle G) using the Law of Sines.

A) 9.86 units

B) 5.76 units

C) 3.33 units

D) 8.86 units

Given a triangle with sides a = 8 units, b = 12 units, and angle C = 110 degrees, find side c using the Law of Cosines.

A) 27.36 units

B) 15.54 units

C) 11.45 units

D) 16.54 units

A triangle with sides of 3, 5, and 7 units. Find the angle between the sides of 3 and 5 units.

A) 150°

B) 60°

C) 120°

D) 90°

Triangle DEF has side DE measuring 6 cm, side EF measuring 9 cm, and the angle between sides DE and EF measures 60 degrees. Find the length of side DF.

A) \$ \sqrt78 \$

B) \$ \sqrt63 \$

C) \$ \sqrt73 \$

D) \$ \sqrt68 \$

Solve triangle ABC, given b = \$3\sqrt2\$, c = 3, and C = 30°. Find angle B.

A) 45°

B) 60°

C) 90°

D) 30°

Triangle JKL has side lengths JK = 7 units, KL = 9 units, and JL = 11 units. Find the measure of angle K.

A) 82.2°

B) 82.8°

C) 72.3°

D) 74.8°

In triangle ABC, side AB measures 7 units, side AC measures 9 units, and angle A measures 120 degrees. Find the length of side BC.

A) \$ \sqrt187 \$

B) \$ \sqrt197 \$

C) \$ \sqrt193 \$

D) \$ \sqrt183 \$