Question

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.

Answer 1

6.44 inches

Explanation:

Answer 2

The length of line segment AC = 6.44 inches

Explanation:

Given as :

ABC is a right angle triangle, right angle at c

So , ∠ ACB = 90°

And ∠ ABC = 40°

So, ∠ BCA = 180° - ( ∠ ACB + ∠ ABC )

Or, ∠ BCA = 180° - ( 90° + 40° )

I.e ∠ BCA = 50°

The length of Hypotenuse = 10 inches

The length of AC = Perpendicular = b

The length of CB = Base = a

∵ This is a right angled Triangle , then

Hypotenuse² = Perpendicular² + Base²

Or, 10² = AC² + BC²

Or, 10² = b² + a² ...1

Now, From triangle ABC

Tan 50° =
`(\textrm BC)/(\textrm AC)`

I.e 1.19 =
`(a)/(b)`

So, a = 1.19 b

From eq 1

10² = b² + (1.19 b)²

Or, 100 = 2.41 b²

so, b² =
`(100)/(2.41)` = 41.49

∴ b =
`√(41.49)` = 6.44 inches

And a = 1.19 × 6.44 = 7.66 inches

Hence The length of line segment AC = 6.44 inches Answer