MATH SOLVE

3 months ago

Q:
# Solve the right triangle ABC, with Cequals90degrees. Aequals58.3degrees, cequals24.8 ft

Accepted Solution

A:

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ftStep-by-step explanation:If ABC is a right triangle, where the right angle is B, thenThe hypotenuse of the triangle is b and a , c are its legssin(A) = [tex]\frac{a}{b}[/tex]sin(C) = [tex]\frac{c}{b}[/tex][tex]b=\sqrt{a^{2}+c^{2}}[/tex]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) = [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 ftm∠B = 31.7° , a = 21.1 ft , b = 13.0 ftLearn more:You can learn more about solving the triangle in brainly.com/question/12985572#LearnwithBrainly