Question

calculator
what is the measure of $\angle c$, to the nearest degree?
$\circ$ $22^\circ$
$\circ$ $43^\circ$
$\circ$ $47^\circ$
$\circ$ $68^\circ$
(there is a triangle abc with side ab = 35, side bc = 45, angle at a is 61°)

Explanation:

Step1: Apply Law of Sines

$\frac{\sin C}{AB} = \frac{\sin A}{BC}$

Step2: Substitute known values

$\frac{\sin C}{35} = \frac{\sin 61^\circ}{45}$

Step3: Isolate $\sin C$

$\sin C = \frac{35 \times \sin 61^\circ}{45}$

Step4: Calculate $\sin C$ value

$\sin C = \frac{35 \times 0.8746}{45} \approx \frac{30.611}{45} \approx 0.6802$

Step5: Find $\angle C$ via arcsine

$\angle C = \arcsin(0.6802) \approx 43^\circ$

Answer:

43°