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.

The length of line segment AC = 6.44 inches

Step-by-step 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° =

I.e 1.19 =

So, a = 1.19 b

From eq 1

10² = b² + (1.19 b)²

Or, 100 = 2.41 b²

so, b² = = 41.49

∴  b = = 6.44 inches

And a = 1.19 × 6.44 = 7.66 inches

Hence The length of line segment AC = 6.44 inches  Answer

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