MATH SOLVE

4 months ago

Q:
# Which equation can be used to find the length of Line segment A C?Triangle A B C is shown. Angle A C B is 90 degrees and angle A B C is 40 degrees. The length of hypotenuse A B is 10 inches, the length of A C is b, and the length of C B is a.

Accepted Solution

A:

Answer:The length of line segment AC = 6.44 inchesStep-by-step explanation:Given as :ABC is a right angle triangle, right angle at cSo , ∠ ACB = 90°And ∠ ABC = 40°So, ∠ BCA = 180° - ( ∠ ACB + ∠ ABC )Or, ∠ BCA = 180° - ( 90° + 40° )I.e ∠ BCA = 50°The length of Hypotenuse = 10 inchesThe length of AC = Perpendicular = b The length of CB = Base = a∵ This is a right angled Triangle , then Hypotenuse² = Perpendicular² + Base²Or, 10² = AC² + BC²Or, 10² = b² + a² ...1Now, From triangle ABCTan 50° = [tex]\frac{\textrm BC}{\textrm AC}[/tex]I.e 1.19 = [tex]\frac{a}{b}[/tex]So, a = 1.19 bFrom eq 110² = b² + (1.19 b)²Or, 100 = 2.41 b²so, b² = [tex]\frac{100}{2.41}[/tex] = 41.49∴ b = [tex]\sqrt{41.49}[/tex] = 6.44 inches And a = 1.19 × 6.44 = 7.66 inches Hence The length of line segment AC = 6.44 inches Answer