Question

Note: Triangle may not be drawn to scale. Suppose a = 7 and c = 12.

Answer 1

To determine the value of b, you can use the Pythagorean theorem:

$c^2=a^2+b^2.$

Substituting a=7, and c=12, you get:

$12^2=7^2+b^2.$

Solving for b, you get:

$\begin{gathered} b^2=12^2-7^2, \\ b=\sqrt{144-49}, \\ b=\sqrt{95}. \end{gathered}$

Now, to determine the measures of angles, A, and B, you can use the trigonometric functions sine and cosine:

$\begin{gathered} sinA=\frac{a}{c}, \\ cosB=\frac{a}{c}. \end{gathered}$

Therefore:

$\begin{gathered} A\approx35.7^{\circ}, \\ B\approx54.3^{\circ}. \end{gathered}$

Answer:

$\begin{gathered} b=9.7, \\ A=35.7^{\circ}, \\ B=54.3^{\circ}. \end{gathered}$