Question

Solve the right triangle​ ABC, with Cequals90degrees. Aequals58.3degrees​, cequals24.8 ft

Answer 1

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

Step-by-step explanation:

If ABC is a right triangle, where the right angle is B, then

• The hypotenuse of the triangle is b and a , c are its legs
• sin(A) = $\frac{a}{b}$
• sin(C) = $\frac{c}{b}$
• $b=\sqrt{a^{2}+c^{2}}$
• The sum of the measures of the two acute angles A and C is 90°

∵ ABC is a right triangle

∵ m∠C = 90°

∴ c is the hypotenuse and a , b are its legs

∵ m∠A = 58.3°

- The sum of the two acute angles in the right triangle = 90°

∴ m∠A + m∠B = 90°

- Substitute the measure of angle A

∴ 58.3 + m∠B = 90

- Subtract 58.3 from both sides

∴ m∠B = 31.7°

∵ sin(A) = $\frac{a}{c}$

∵ c = 24.8 feet

∴ sin(58.3) = $\frac{a}{24.8}$

- By using cross multiplication

∴ a = (24.8) × sin(58.3)

∴ a = 21.1 ft

∵ sin(B) = $\frac{b}{c}$

∵ c = 24.8 feet

∴ sin(31.7) = $\frac{b}{24.8}$

- By using cross multiplication

∴ b = (24.8) × sin(31.7)

∴ b = 13.0 ft

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

Learn more:

You can learn more about solving the triangle in brainly.com/question/12985572

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