Question

15 find the length of side x, using trig ratios (soh - cah - toa): a 13 cos (60)=6.50 b 13 sin (60)=11.26 c 13 tan (60)=22.52 d 26.00 16 find the length of side x using trig ratios (soh - cah - toa): a 14 cos 48 = 9.37 b 14/(sin 48)=18.84 c 14 sin 48 = 10.40 d 14 tan 48 = 15.55

Explanation:

Step1: Identify trig - ratio for first triangle

In the first right - triangle, the side adjacent to the 60° angle is 13 cm and we want to find the opposite side $x$. We use the tangent ratio $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan(60^{\circ})=\frac{x}{13}$, and $x = 13\tan(60^{\circ})$.

Step2: Identify trig - ratio for second triangle

In the second right - triangle, the hypotenuse is 14 and we want to find the side opposite the 48° angle. We use the sine ratio $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin(48^{\circ})=\frac{x}{14}$, and $x = 14\sin(48^{\circ})$.

Answer:

For the first triangle: C. $13\tan(60)=22.52$
For the second triangle: C. $14\sin(48)=10.40$