Solve the right triangle. If two sides are given, give angles in degrees and minutes.
-$$\mathrm { a } = 2.6 \text { in., } \mathrm { A } = 48.5 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }$$
Round values to one decimal place.
A) $b = 1.2$ in., $B = 41.5 ^ { \circ } , c = 2.9$ in.
B) $b = 4.2$ in., $B = 41.5 ^ { \circ } , c = 4.9$ in.
C) $b = 2.3$ in., $B = 41.5 ^ { \circ } , c = 3.5$ in.
D) $b = 4.2$ in., $B = 41.5 ^ { \circ } , c = 3.5$ in.

Question

Quizplus · Accepted Answer

To solve the triangle, use the angle sum property: $B = 90^\circ - 48.5^\circ = 41.5^\circ$. Use the sine rule to find $b$: $b = a \cdot \tan(B) = 2.6 \cdot \tan(41.5^\circ) \approx 2.3$ in. Use the Pythagorean theorem to find $c$: $c = \sqrt{a^2 + b^2} = \sqrt{2.6^2 + 2.3^2} \approx 3.5$ in.

Solve the Right Triangle a=2.6 in., A=48.5∘,C=90∘\mathrm { a } = 2.6 \text { in., } \mathrm { A } = 48.5 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }a=2.6 in., A=48.5∘,C=90∘

Solve the Right Triangle $\mathrm { a } = 2.6 \text { in., } \mathrm { A } = 48.5 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }$