solve the triangle.\nwrite each answer as an integer or as a decimal rounded to the nearest tenth.
solve the triangle.\nwrite each answer as an integer or as a decimal rounded to the nearest tenth.
Answer
Explanation:
Step1: Find angle Q
The sum of angles in a triangle is $180^\circ$. $\angle Q = 180^\circ - 45^\circ - 82^\circ = 53^\circ$
Step2: Find side $s$ via Law of Sines
Relate $s$, $\angle S$, $r$, $\angle R$. $\frac{s}{\sin(45^\circ)} = \frac{7}{\sin(82^\circ)}$ $s = \frac{7\sin(45^\circ)}{\sin(82^\circ)} \approx \frac{7 \times 0.7071}{0.9903} \approx 5.0$
Step3: Find side $q$ via Law of Sines
Relate $q$, $\angle Q$, $r$, $\angle R$. $\frac{q}{\sin(53^\circ)} = \frac{7}{\sin(82^\circ)}$ $q = \frac{7\sin(53^\circ)}{\sin(82^\circ)} \approx \frac{7 \times 0.7986}{0.9903} \approx 5.6$
Answer:
$\angle Q = 53^\circ$, $s \approx 5.0$, $q \approx 5.6$