Problem

For the triangle shown, \(a~=~7\), \(b~=~9\), and included angle \(C~=~50°\). Find \(\text{all}~\text{three}~\text{angles}\) and side lengths, then verify the angle sum and opposite side-angle relationships.

Prompt SAS triangle with sides a=7 and b=9 and included angle C=50°; side c and angles A and B are withheld.

Answer choices

Choose your path.

Preview only

c²=7²+9²-2·7·9cos(50°), so c≈7.0. Then A≈50.0° and B≈80.0°; the angles total 180° and the rounded equal sides a and c match the rounded equal angles A and C.

Use c=|9-7|=2.0 and report A=50.0°, B=80.0°, and C=50.0°, even though equal angles do not have equal opposite sides.

Use c≈7.0 but swap the opposite-angle matches, reporting A≈80.0°, B≈50.0°, and C=50.0°.

Use a plus sign: c²=7²+9²+2·7·9cos(50°), so c≈14.5; then A≈21.7° and B≈108.3°.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

For the triangle shown, \(a~=~7\), \(b~=~9\), and included angle \(C~=~50°\). Find \(\text{all}~\text{three}~\text{angles}\) and side lengths, then verify the angle sum and opposite side-angle relationships.

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.