Question

Solve the triangle for all missing sides and angles

Answer 1

B = 59

a = 9.01

c = 17.49

Explanation:

Angle B

180 - 90 - 31 = 59

c

The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.

sin(B)=opp/hyp

sin(B)=15/c

sin(59)=15/c

c=15/sin(59)

c=17.49

Find the last side of the triangle using the Pythagorean theorem.

`a^(2) +b^(2) =c^(2) \\a^(2) +15^(2) =17.49^(2) \\\\a^(2) =17.49^(2) -15^(2)\\a=9.01`

Answer 2

a=9

c= 17.5

angles: a =31, b =59, c =90

Explanation:

a:

tan (31) = a/15 *cross multiply*

a = 15 (tan (31))

a = 9

c:

*use pythagorean theorum*

9^2 + 15^2 = c^2

81 + 225 = c^2

306 = c^2

17.5 = c