Question

choose the correct values for x and y in the right triangle. x = 11 y = 22 x = \frac{11\sqrt{3}}{3} y = 11\sqrt{3}

Explanation:

Step1: Use sine function for x

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here $\theta = 30^{\circ}$ and hypotenuse is 22. So $\sin30^{\circ}=\frac{x}{22}$, and since $\sin30^{\circ}=\frac{1}{2}$, we have $x = 22\times\sin30^{\circ}=22\times\frac{1}{2}=11$.

Step2: Use cosine function for y

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 30^{\circ}$ and hypotenuse is 22. So $\cos30^{\circ}=\frac{y}{22}$, and since $\cos30^{\circ}=\frac{\sqrt{3}}{2}$, we have $y = 22\times\cos30^{\circ}=22\times\frac{\sqrt{3}}{2}=11\sqrt{3}$.

Answer:

x = 11
y = 11√3