Plane trigonometry, by S.L. Loney.

[Exs. XXX.] SOLUTION OF TRIANGLES.

199

9. If a =2, b = 1 +/3, and C= 60~, solve the triangle.
10. Two sides of a triangle are X/3 + 1 and,/3 - 1, and the included
angle is 60~; find the other side and angles.
11. If b = 1, c =,/3 - 1, and A = 60~, find the length of the side a.
Ad 17
12. If b=91, c 125 and tan- = -7, prove that a = 204.
2 6
31
13. If a= 5, b= 4, and cos (A - B) = 2, prove that the third side c will
be 6.
14. One angle of a triangle is 30~ and the lengths of the sides
adjacent to it are 40 and 40 /3 yards. Find the length of the third
side and the number of degrees in the other angles.
15. The sides of a triangle are 9 and 3, and the difference of the
angles opposite to them is 90~. Find the base and the angles, having
given
log 2 =-30103, log 3 =4771213,
log 75894=4-8802074, log 75895 =4-8802132,
L tan 26~ 33'= 9-6986847
and L tan 26~ 34' = 96990006.
16. Two sides of a triangle are 237 and 158 feet and the contained
angle is 66~ 40'; find the base and the other angles, having given
log 2 = -30103, log 79 = 1-89763,
log 22687 = 435578, L cot 33~ 20'= 10-18197
L sin 33~ 20' = 973998, L tan 16~ 54' = 9 -48262,
L tan 16~ 55'= 9-48308, L sec 16~ 54'= 10-01917,
and L sec 16~ 55' = 10-01921.
rn i, B-C b+c. A]
Use the formula cos -- sin.
[ 2 a 2 '_
a-b C'
17. If tan 0= a-bcot,. C
sin -
prove that c = (a+ b) -—.
cos e