Question

GIVING MEDALS
in right triangle ABC, A=76 degrees, a=13 an 12 years ago

Answer 1

for the angles, you know A= 76, C = 90, that would leave B= 14

i found this with the angle sum, all angles of a triangle add to be 180. so

76 + 90 + B = 180

166+ B = 180

B = 14

now for the angles, use the law of sines. which is (sin A)/(a) = (sin B)/(b) = (sin C)/(c)

since you know angle A and side a and Angle B, find side b

(sin A)/(a) = (sin B)/(b)

(sin 76)/(13) = (sin 14)/(b)

b*sin 76 = 13*sin 14

b = (13*sin 14)/(sin 76)

b = 3.24

use Pythagorean theorem to solve for side c

a^2 + b^2 = c^2

13^2 + 3.24^2 = c^2

179.50 = c^2

√179.50 = c

13.40 = c

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