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# Geometry question i need help with asap please?

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What is the length of AB¯¯¯¯¯, to the nearest tenth of a centimeter?

10.5 cm

13.7 cm

15.7 cm

17.9 cm

Jun 2, 2018

#1
+2340
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This problem is a simple example of the application of the law of sines. The law of sines relates the sine of an angle of an oblique triangle to its opposite side length via proportions.

$$\frac{\sin A}{a}=\frac{\sin C}{c}$$

 $$\frac{\sin 42}{12}=\frac{\sin 50}{AB}$$ Cross multiply to solve for the missing value. $$AB\sin 42=12\sin 50$$ $$AB=\frac{12\sin 50}{\sin 42}\approx 13.7\text{cm}$$
Jun 2, 2018

#1
+2340
+1
$$\frac{\sin A}{a}=\frac{\sin C}{c}$$
 $$\frac{\sin 42}{12}=\frac{\sin 50}{AB}$$ Cross multiply to solve for the missing value. $$AB\sin 42=12\sin 50$$ $$AB=\frac{12\sin 50}{\sin 42}\approx 13.7\text{cm}$$