Question

what is the value of y to the nearest hundredth? 10 48° y 14.94 11.11 6.69 7.43

Explanation:

Step1: Identify trigonometric ratio

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 48^{\circ}$, the adjacent side to the angle $\theta$ is $y$ and the hypotenuse is 10. So, $\cos48^{\circ}=\frac{y}{10}$.

Step2: Solve for $y$

Multiply both sides of the equation $\cos48^{\circ}=\frac{y}{10}$ by 10. We get $y = 10\times\cos48^{\circ}$.
We know that $\cos48^{\circ}\approx0.6691$. Then $y=10\times0.6691 = 6.691\approx6.69$.

Answer:

6.69