7. Non-Right Triangles

In triangle $BCD$, which is isosceles with $BC$ congruent to $BD$, what is the measure of angle $CBD$ if angle $C$ is $20°$? Choose the correct answer.

In triangle $\mathrm{ABC}$, if side $\mathrm{AB}$ has length $b$, side $\mathrm{BC}$ has length $a$, and the angle at vertex $C$ is $\gamma$, what is the length of side $\mathrm{AC}$ according to the Law of Cosines?

Solve each triangle. Approximate values to the nearest tenth.

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Solve each triangle. See Examples 2 and 3.

C = 45.6°, b = 8.94 m, a = 7.23 m

A surveyor wishes to find the distance across a river while standing on a small island. If she measures distances of $a=30m$ to one shore, $c=60m$ to the opposite shore, and an angle of $B=100\(\degree\)$ between the two shores, find the distance between the two shores.

Solve each triangle. See Examples 2 and 3.

a = 9.3 cm, b = 5.7 cm, c = 8.2 cm

Solve each triangle. See Examples 2 and 3.

B = 74.8°, a = 8.92 in., c = 6.43 in.

In oblique triangle ABC, C = 68°, a = 5, and b = 6. Find c to the nearest tenth.

In Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit.

a = 11 yards, b = 9 yards, c = 7 yards

Solve each triangle. See Examples 2 and 3.

A = 41.4°, b = 2.78 yd, c = 3.92 yd

In Exercises 1–12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state 'no triangle.' If two triangles exist, solve each triangle. B = 66°, a = 17, c = 12

In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.

a = 63, b = 22, c = 50