Question

solve for y. do not convert your answer to decimal form.
draw
(right triangle with hypotenuse 8, angle 60° at the base, base length y)
show your work here
hint: to add the square root symbol (√), type
oot\

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle with hypotenuse \(c = 8\) and we want to find the adjacent side \(y\) to the \(60^{\circ}\) angle. The cosine of an angle in a right - triangle is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(60^{\circ})=\frac{y}{8}\).

Step2: Recall the value of \(\cos(60^{\circ})\)

We know that \(\cos(60^{\circ})=\frac{1}{2}\). Substituting this value into the equation \(\cos(60^{\circ})=\frac{y}{8}\), we get \(\frac{1}{2}=\frac{y}{8}\).

Step3: Solve for \(y\)

To solve for \(y\), we can cross - multiply. Cross - multiplying gives us \(y = 8\times\frac{1}{2}\).

Answer:

\(y = 4\)