Solve the right triangle.
-$$\mathrm { a } = 2.2 \text { in., } \mathrm { A } = 59.4 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }$$
Round values to one decimal place.
A) $b = 0.2$ in., $B = 30.6 ^ { \circ } , c = 2.2$ in.
B) $b = 1.3$ in., $B = 30.6 ^ { \circ } , c = 2.6$ in.
C) $b = 2.7$ in., $B = 30.6 ^ { \circ } , c = 3.5$ in.
D) $b = 2.7$ in., $B = 30.6 ^ { \circ } , c = 2.6$ in.

Question

Quizplus · Accepted Answer

To solve the right triangle, we use trigonometric ratios and the fact that the sum of angles in a triangle is 180 degrees. Given $a = 2.2$ in and $A = 59.4^\circ$, and knowing $C = 90^\circ$, we can find $B = 180^\circ - 90^\circ - 59.4^\circ = 30.6^\circ$. To find $b$ and $c$, we can use the sine and cosine functions respectively:$$b = a \cdot \tan(A) = 2.2 \cdot \tan(59.4^\circ) \approx 1.3$$ in,$$c = a / \cos(A) = 2.2 / \cos(59.4^\circ) \approx 2.6$$ in.Thus, option B is correct.

Solve the Right Triangle a=2.2 in., A=59.4∘,C=90∘\mathrm { a } = 2.2 \text { in., } \mathrm { A } = 59.4 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }a=2.2 in., A=59.4∘,C=90∘

Solve the Right Triangle $\mathrm { a } = 2.2 \text { in., } \mathrm { A } = 59.4 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }$