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# trig question

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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