Question

HELP! Use trigonometric ratios to determine whether or not it is possible to construct triangle ABC if b = 3, c = 5, and B = 45°. In your final answer, include all of your calculations. WILL GIVE BRAINLIEST TO WHOEVER SHOWS ALL THE CORRECT CALCULATIONS!

Answer 1

Let's try to solve the triangle and see what happens.

The Law of Sines gives angle C:

$\dfrac{\sin C}{c} = \dfrac{\sin B}{b}$

$\sin C = \dfrac{c \sin B}{b}$

See where this is going?

$\sin C = \dfrac{ 5(\sin 45)}{3} = \frac 5 3 (\sqrt{2}/2) = \frac 5 6 \sqrt{2} \approx 1.2$

That sine is greater than one so there are no such possible triangles.