7. Non-Right Triangles

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.

Use the Law of Cosines to find the angle $C$, rounded to the nearest tenth.



Solve the triangle: $b=5,c=3,A=100\degree$.

Solve the triangle: $a=5$, $b=15$, $c=13$.

Solve each triangle. See Examples 2 and 3.

a = 3.0 ft, b = 5.0 ft, c = 6.0 ft

CONCEPT PREVIEW Assume a triangle ABC has standard labeling.

a. Determine whether SAA, ASA, SSA, SAS, or SSS is given.

b. Determine whether the law of sines or the law of cosines should be used to begin solving the triangle.

a, b, and C

Solve each triangle. Approximate values to the nearest tenth.

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Solve each triangle. Approximate values to the nearest tenth.

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Solve each triangle. Approximate values to the nearest tenth.

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Solve each triangle. See Examples 2 and 3.

A = 41.4°, b = 2.78 yd, c = 3.92 yd

Solve each triangle. See Examples 2 and 3.

C = 45.6°, b = 8.94 m, a = 7.23 m

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.

a = 42.9 m, b = 37.6 m, c = 62.7 m

Solve each triangle. See Examples 2 and 3.

a = 965 ft, b = 876 ft, c = 1240 ft

Solve each triangle. See Examples 2 and 3.

A = 80° 40', b = 143 cm, c = 89.6 cm

Solve each triangle. See Examples 2 and 3.

B = 74.8°, a = 8.92 in., c = 6.43 in.

Solve each triangle. See Examples 2 and 3.

A = 112.8°, b = 6.28 m, c = 12.2 m

CONCEPT PREVIEW Assume a triangle ABC has standard labeling.

a. Determine whether SAA, ASA, SSA, SAS, or SSS is given.

b. Determine whether the law of sines or the law of cosines should be used to begin solving the triangle.

a, B, and C

A plane has an airspeed of 520 mph. The pilot wishes to fly on a bearing of 310°. A wind of 37 mph is blowing from a bearing of 212°. In what direction should the pilot fly, and what will be her ground speed?

Find the force required to keep a 75-lb sled from sliding down an incline that makes an angle of 27° with the horizontal. (Assume there is no friction.)

Find the exact area of each triangle using the formula 𝓐 = ½ bh, and then verify that Heron's formula gives the same result.

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Find the area of each triangle ABC.

a = 76.3 ft, b = 109 ft, c = 98.8 ft

Find the length of the remaining side of each triangle. Do not use a calculator.

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