Question

1. 19 32° x 44) 49° x 11

Explanation:

Step1: Identify trig - function for first triangle

In the first right - triangle with hypotenuse 19 and an angle of 32°, and we want to find the side opposite the 32° angle. We use the sine function. $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin(32^{\circ})=\frac{x}{19}$.

Step2: Solve for x in first triangle

$x = 19\times\sin(32^{\circ})$. Since $\sin(32^{\circ})\approx0.5299$, then $x = 19\times0.5299 = 10.0681\approx10.07$.

Step3: Identify trig - function for second triangle

In the second right - triangle with an angle of 49° and adjacent side 11, and we want to find the opposite side x. We use the tangent function. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan(49^{\circ})=\frac{x}{11}$.

Step4: Solve for x in second triangle

$x = 11\times\tan(49^{\circ})$. Since $\tan(49^{\circ})\approx1.1504$, then $x = 11\times1.1504 = 12.6544\approx12.65$.

Answer:

For the first triangle, $x\approx10.07$. For the second triangle, $x\approx12.65$.