Questions: Law of sine 5) m angle C=18°, b=26 ft, c=11 ft 6) m angle C=88°, m angle A=65°, c=11 yd 7) m angle A=116°, c=12 ft, a=35 ft 8) m angle A=31°, c=29 in, a=28 in 9) m angle B=34°, b=33 cm, a=24 cm 10) m angle B=157°, a=22 ft, b=7 ft

Solution Steps

Given:

• \( m \angle C = 18^\circ \)
• \( b = 26 \, \text{ft} \)
• \( c = 11 \, \text{ft} \)

The Law of Sines states: \[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]

For this problem, we use: \[ \frac{b}{\sin B} = \frac{c}{\sin C} \]

Substitute the known values: \[ \frac{26}{\sin B} = \frac{11}{\sin 18^\circ} \]

Solve for \(\sin B\): \[ \sin B = \frac{26 \cdot \sin 18^\circ}{11} \]

Given:

• \( m \angle C = 88^\circ \)
• \( m \angle A = 65^\circ \)
• \( c = 11 \, \text{yd} \)

First, find \( m \angle B \): \[ m \angle B = 180^\circ - m \angle A - m \angle C = 180^\circ - 65^\circ - 88^\circ \]

Use the Law of Sines: \[ \frac{a}{\sin A} = \frac{c}{\sin C} \]

Substitute the known values: \[ \frac{a}{\sin 65^\circ} = \frac{11}{\sin 88^\circ} \]

Solve for \( a \): \[ a = \frac{11 \cdot \sin 65^\circ}{\sin 88^\circ} \]

Given:

• \( m \angle A = 116^\circ \)
• \( c = 12 \, \text{ft} \)
• \( a = 35 \, \text{ft} \)

First, find \( m \angle C \) using the Law of Sines: \[ \frac{a}{\sin A} = \frac{c}{\sin C} \]

Substitute the known values: \[ \frac{35}{\sin 116^\circ} = \frac{12}{\sin C} \]

Solve for \(\sin C\): \[ \sin C = \frac{12 \cdot \sin 116^\circ}{35} \]

Find \( m \angle C \) using the inverse sine function.

Final Answer