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
∵ 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) = [tex]\frac{a}{c}[/tex]
∵ c = 24.8 feet
∴ sin(58.3) = [tex]\frac{a}{24.8}[/tex]
- By using cross multiplication
∴ a = (24.8) × sin(58.3)
∴ a = 21.1 ft
∵ sin(B) = [tex]\frac{b}{c}[/tex]
∵ c = 24.8 feet
∴ sin(31.7) = [tex]\frac{b}{24.8}[/tex]
- 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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