Given the indicated parts of triangle ABC with 𝛾 = 90°, approximate the remaining parts. (Round your answers to the nearest tenth.)

Question

Given the indicated parts of triangle ABC with 𝛾 = 90°, approximate the remaining parts. (Round your answers to the nearest tenth.)

a = 31,    b = 9.0

𝛼	=	°
𝛽	=	°
c	=

Answer 1

a^2+b^2=c^2

961+81=1042^.5=32.28=c

a/sin𝛼=b/sin𝛽=c; Sin of a rt angle=1.

31/sin𝛽=9/sin𝛼=32.28

31/.96; 𝛽=73.811°

90-73.811=16.189=𝛼

Answer 2

β = 90 -31 = 59

Law of Sines

9/sin 59 = a/sin 31

Once you have a, the Pythagorean Theorem will get you c.