Question

State whether the given measurements determine zero, one, or two triangles. A = 58°, a = 25, b = 28

Answer 1

1

Explanation:

I believe it is 1. Just picture or draw a diagram of the constraints. Don't quote me on this though...

Answer 2

Explanation:

apply sine formula

`(a)/(sin ~A) =(b)/(sin~B) \\(25)/(sin~58) =(28)/(sin ~B) \\sin~B=(28)/(25) * sin~58\\B=sin^(-1) ((28)/(25) * sin ~58)=71.77 \approx 72 ^\circ`

so third angle=180-(58+72)=180-130=50°

∠C=50°

`cos ~C=(a^2+b^2-c^2)/(2ab) \\or ~2abcos~C=a^2+b^2-c^2\\2*25*28*cos ~50=25^2+28^2-c^2\\c^2=625+784-1400 *cos~50\\c^2=1409-899.90\\c^2=509.1\\c=√(509.1) \approx 22.56 \approx 22.6`

so one triangle is formed.