Question

solve the triangle shown to the right
a≈□°
(simplify your answer)
a≈□
(type an integer or decimal rounded to two decimal places as needed)
b≈□
(type an integer or decimal rounded to two decimal places as needed)

Explanation:

Step1: Find angle \( A \)

The sum of angles in a triangle is \( 180^{\circ} \). So \( A=180^{\circ}-(95^{\circ} + 60^{\circ})\)
\(A = 25^{\circ}\)

Step2: Use the Law of Sines to find \( a \)

The Law of Sines states \(\frac{a}{\sin60^{\circ}}=\frac{7}{\sin25^{\circ}}\)
\(a=\frac{7\times\sin60^{\circ}}{\sin25^{\circ}}\)
\(\sin60^{\circ}=\frac{\sqrt{3}}{2}\approx0.8660\), \(\sin25^{\circ}\approx0.4226\)
\(a=\frac{7\times0.8660}{0.4226}\approx14.39\)

Step3: Use the Law of Sines to find \( b \)

By the Law of Sines \(\frac{b}{\sin95^{\circ}}=\frac{7}{\sin25^{\circ}}\)
\(\sin95^{\circ}\approx0.9962\)
\(b = \frac{7\times\sin95^{\circ}}{\sin25^{\circ}}=\frac{7\times0.9962}{0.4226}\approx16.51\)

Answer:

\(A\approx25^{\circ}\)
\(a\approx14.39\)
\(b\approx16.51\)