Checking work on triangles
Can someone check over my work?
Lookouts in two fire towers, A and B located 10km apart sight a forest fire. Electronic equipment allows them to determine that the fire is at an angle of 71 from tower a and 100 from tower b. Which tower is closer to the fire and how far away is it.
I drew a triangle with the information and did 71+100= 171-180=9 for angle C. So I got A=71, B=100, and C=9 then I used the A=10sin(100)/sin(9) and got 62.95 (rounded)
2. On a baseball diamond with 90-ft sides, the pitcher's mound is 60.5 feet from home plate. How far is it from the pitcher's mound to third base?
I made a picture of it and then found the following angles 45,90,45 and the hyp is 90, adj is 60.5 and then I did the a square + b square= c square and found 66.63 (rounded) did I do this right?
3. Solve the equation 2sin x- (square root 3)- 0 for exact value of x in [0,2pie).
I got pie/6, 5pie/6 for this did I do it right? I moved the square root of 3 over and then divided by the 2 and then found sin.