Question

Solve each triangle.

$a=3,c=2,B=90°$

Short answer

The solution is$b\approx 3.6,A\approx 56.3°,C\approx 33.7°$.

Step-by-step solution

Step 1. Given information 

$a=3,c=2,B=90°$

Step 2. Calculation 

Use Law of Cosines -

$b^2=a^2+c^2-2ac\cos B$

$=9+4-2\times 3\times 2\cos 90°$

$=13-12\times 0$

$b\approx 3.6$

For C:

$c^2=a^2+b^2-2ab\cos C$

localid="1646896357731" $\cos C=\frac{a^2+b^2-c^2}{2ab}\approx \frac{9+12.96-4}{2\times 3\times 3.6}\approx \frac{17.96}{21.6}$

$C\approx {\cos }^{-1}\frac{17.96}{21.6}\approx 33.7°$

Since we know B and C,

$A=180°-90°-33.7°\approx 56.3°$