Question

I . Given triangle ABC with A = 32° , B = 105°, and b = 25 inches, find the length of side a. Round to the nearest tenth. Hint: This is not a right triangle. You'll need to use the Law of Sines or Law of Cosines to solve for the missing side. If you're not sure which, draw the triangle and see whether you have ASAAAS (Law of Sines) or SAS/SSS (Law of Cosines).

Answer 1

Law of sines,

$\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}$

But we need only this for solve to the question

$\frac{sinA}{a}=\frac{sinB}{b}$

We have to find length of a

Now, by putting values of A, B and b

$\frac{sin32^{\circ}}{a}=\frac{sin105^{\circ}}{25}$

$\frac{0.5299}{a}=\frac{0.9659}{25}$

$a=\frac{25*0.5299}{0.9659}$

$a=\frac{13.2475}{0.9659}$

$a=13.7151$

So length of a is 13.71 inches.