Mastering Triangle Problems: Sines & Cosines for 10th Graders

A triangle has two sides measuring 8 cm and 10 cm, with an included angle of 45 degrees. Calculate the length of the third side using the law of cosines.

• c ≈ 5.00 cm

• c ≈ 9.50 cm

• c ≈ 12.00 cm

• c ≈ 7.07 cm

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In triangle ABC, angle A measures 30 degrees, side a is 12 cm, and side b is 15 cm. Find the measure of angle B using the law of sines.

• 45 degrees

• 60 degrees

• 38.68 degrees

• 25 degrees

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

A boat sails from point A to point B, creating a triangle with point C. If AC = 5 km, BC = 7 km, and angle A = 60 degrees, find the length of AB using the law of cosines.

• 8.00 km

• 7.50 km

• 5.00 km

• 6.24 km

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In triangle XYZ, side x = 14 m, side y = 10 m, and angle Z = 50 degrees. Calculate the measure of angle Y using the law of sines.

• 40 degrees

• 60 degrees

• 20 degrees

• 30 degrees

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In triangle DEF, angle D is 45 degrees, side d is 10 m, and side e is 12 m. Calculate the measure of angle E using the law of sines.

• 35.0 degrees

• 25.0 degrees

• 50.0 degrees

• 60.0 degrees

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

A surveyor measures a triangle with sides of lengths 20 m and 25 m, and the included angle is 70 degrees. Find the length of the third side using the law of cosines.

• 26.12 m

• 22.75 m

• 30.00 m

• 24.50 m

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In triangle PQR, side p = 9 cm, side q = 12 cm, and angle R = 40 degrees. Calculate the measure of angle Q using the law of sines.

• Q = 50 degrees

• Q = 75 degrees

• Q = 62.3 degrees

• Q = 45 degrees

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In triangle GHI, angle G = 35 degrees, side g = 18 m, and side h = 22 m. Find the measure of angle H using the law of sines.

• 75 degrees

• 48.6 degrees

• 30 degrees

• 60 degrees

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11