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Trigonometry
Question

Find all missing side and angle of the triangle. If there are two solutions,given both if there is no triangle,state this and indicate how you know A=40 °, a=8, b=10

2. Find all missing sides and angles of the triangle. If there are two solutions, give both. If there is no triangle, state this and indicate how you know.

$$A = 40 ^ { \circ } , a = 8 , b = 10$$

(5 points)

Acute Scalene Triangle Side $$a = 8$$ Side $$b = 10$$

Side $$c = 12.42305$$

Angle $$\angle A = 40 ^ { \circ } = 0.69813 rad = 2 / 9 \pi$$

Angle $$\angle B = 53.464 ^ { \circ } = 53 ^ { \circ } 27 ^ { \prime } 51 ^ { \prime \prime } = 0.93313 rad$$

Angle $$\angle C = 86.536 ^ { \circ } = 86 ^ { \circ } 32 ^ { \prime } 9 ^ { \prime \prime } = 1.51034 rad$$

Obtuse Scalene Triangle Side $$a = 8$$ Side $$b = 10$$

Side $$c = 2.89784$$

Angle $$\angle A = 40 ^ { \circ } = 0.69813 rad = 2 / 9 \pi$$

Angle $$\angle B = 126.536 ^ { \circ } = 126 ^ { \circ } 32 ^ { \prime } 9 ^ { \prime \prime } = 2.20847 rad$$

Angle $$\angle C = 13.464 ^ { \circ } = 13 ^ { \circ } 27 ^ { \prime } 51 ^ { \prime \prime } = 0.23499 rad$$

Solution
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