Answer each question in full ASAP please

Question

1).

find the area of a triangle with B=18.2 degrees, a=34, and c=37. Just type the number (rounded to the nearest tenth) in the blank.

2.)

a man begins at the base of a mountain at point A and walks 5 miles up the side of the mountain at a 40 degree incline. He then walks down a 30 degree incline to point B at the base of the mountain on the other side. If the highway department wants to dig a straight tunnel from point A to point B, how long will the tunnel be?

4.)

given that the area of a triangle ABC is 13 cm^2, and b=7 and c=4, determine the two possible values for angle A.

Answer 1

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°.