Question

Given: A=38 degrees, a=12cm and b=10cm find the remaining parts

Answer 1

Answer on Question #46559 – Math – Geometry

Given: A=38 degrees, a=12cm and b=10cm find the remaining parts

Solution:

According to the theorem of sines:

$$\begin{array}{l} \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \\ \frac{a}{\sin A} = \frac{b}{\sin B} \\ \frac{12}{\sin 38{}^\circ} = \frac{10}{\sin B} \\ \sin B = \frac{10 * \sin 38{}^\circ}{12} = \frac{10 * 0.6157}{12} = 0.5131 \\ B = 31{}^\circ \\ A + B + C = 180{}^\circ \\ C = 180{}^\circ - A - B = 180{}^\circ - 38{}^\circ - 31{}^\circ = 111{}^\circ \\ \frac{b}{\sin B} = \frac{c}{\sin C} \\ \frac{10}{0.5131} = \frac{c}{0.9336} \\ c = \frac{10 * 0.9336}{0.5131} = 18.195 \text{ cm} \end{array}$$

Answer:

c=18.195cm

B=31°

C=111°

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