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AB = 20 cm, m angle A = 30 degrees, and m angle C = 40 degrees. Express the number of centimeters in the length of line BC.

 

 Feb 15, 2022
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Draw a vertical line from B. Label the point where it intersects AC point D.

 \(\triangle{ABD}\) is a 30-60-90 triangle. This means that BD is 10.

Using the Pythagorean Theorem, you find that AD is equal to \(\sqrt{300} = 10\sqrt3\).

To find DC, we need to use trig.

We use sin \(({\text{opposite}\over\text{hypotenuse}})\), and have: \({\sin(40)}={10\over{BC}}\)

This means that \(\color{brown}\boxed{BC \approx 15.55723}\)

 Feb 15, 2022

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