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

Answer:

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° = $\frac{\textrm BC}{\textrm AC}$

I.e 1.19 = $\frac{a}{b}$

So, a = 1.19 b

From eq 1

10² = b² + (1.19 b)²

Or, 100 = 2.41 b²

so, b² = $\frac{100}{2.41}$ = 41.49

∴  b = $\sqrt{41.49}$ = 6.44 inches

And a = 1.19 × 6.44 = 7.66 inches

Hence The length of line segment AC = 6.44 inches  Answer

Answer 2

Answer:

6.44 inches

Step-by-step explanation: