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∆ABC

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» Using the figure below, solve the required unknown value of right triangle ABC.

#1 (If A=15° and c=37, find a)

• cos θ = adjacent/hypothenuse
• cos A = a/c
• cos 15° = a/37
• a = 37 (cos 15°)
• a = 35.74

ANSWER: a = 35.74

#2 (If A=76° and a=13, find b)

• tan θ = opposite/adjacent
• tan A = b/a
• tan 76° = b/13
• b = 13 (tan 76°)
• b = 52.14

ANSWER: b = 52.14

#3 (If a=13 and B=16°, find c)

• sin θ = opposite/hypothenuse
• sin B = a/c
• sin 16° = 13/c
• c = 13 / (sin 16°)
• c = 47.16

ANSWER: c = 47.16

#4 (If b=10 and c=20, find m∠A)

• sin θ = opposite/hypothenuse
• sin A = b/c
• sin A = 10/20
• sin A = 0.5
• A = sin^(-1) (0.5)
• A = 30°

ANSWER: m∠A = 30°

#5 (If a=7 and b=11, find m∠B)

• tan θ = opposite/adjacent
• tan B = a/b
• tan B = 7/11
• B = tan^(-1) (7/11)
• B = 32.47°

ANSWER: m∠B = 32.47°

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