solve the right triangle.\nround your answers to the nearest tenth.\n$a = \\square^\\circ$\n$a =…
solve the right triangle.\nround your answers to the nearest tenth.\n$a = \\square^\\circ$\n$a = \\square$\n$b = \\square$
Answer
Explanation:
Step1: Calculate angle $A$
Sum of triangle angles is $180^\circ$. $A = 180^\circ - 90^\circ - 49^\circ = 41^\circ$
Step2: Calculate side $a$
Use cosine of $49^\circ$. $\cos(49^\circ) = \frac{a}{30} \implies a = 30 \times \cos(49^\circ) \approx 30 \times 0.6561 = 19.7$
Step3: Calculate side $b$
Use sine of $49^\circ$. $\sin(49^\circ) = \frac{b}{30} \implies b = 30 \times \sin(49^\circ) \approx 30 \times 0.7547 = 22.6$
Answer:
$A = 41^\circ$ $a = 19.7$ $b = 22.6$