Question

Find all solutions for a triangle with C=17%, a=10, and c=11. Round to the nearest tenth.

Answer 1

I'll assume that's C=17 degrees, a=10, c=11.

Law of sines says

$\dfrac{a}{\sin A} = \dfrac{c}{\sin C}$

$\sin A = \dfrac{a}{c} \sin C$

$\sin A = \dfrac{10}{11} \sin 17^\circ=0.265792$

$A = \arcsin 0.265792 = 15.414^\circ \textrm{ or }164.586^\circ$

We get supplementary angles for the inverse sine.

We can ignore the larger one because 164.5+17>180 so not a valid traingle.

$A= 15.414^\circ, \quad B = 180^\circ - A - C = 147.586^\circ$

$b = \dfrac{c\sin B}{\sin C}= \dfrac{11 \sin 147.586^\circ}{\sin 17^\circ} = 20.1674$

Rounding,

Answer: A=15.4°, B=147.6°, b=20.2

Answer 2

I feel like the correct answer is C