Alan G. answered • 07/20/16

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Hannah,

1) Use the formula Area = ½ ac sin B: Area = ½ (34)(37) sin 18.2° ≈ 196.5

2) This question is asking for the length of the base c of a triangle with angle A = 40°, angle B = 30°, and side b = 5. The top angle is C, and will equal C = 180° − A − B = 180° − 40° − 30° = 110°. You can now use the Law of Sines to solve for side c:

c/sin C = b/sin B

c/sin 110° = 5/sin 30° = 5/½ = 10

c = 10/sin 110° ≈ 10.6 miles

3) Again, you can use a formula similar to that in 1), which is Area = ½ bc sin A.

13 = ½ (7)(4) sin A

sin A = 26/28 = 13/14.

One answer is sin

^{-1}(13/14) and the other is the supplement of the first answer.After computing to one decimal place, the answers are

A = 68.2° and 111.8°.