Question

find y.
30°
60°
3 m
y
write your answer in simplest radical form.
meters
submit

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, we can use the tangent function. The tangent of an angle in a right - triangle is defined as \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 30^{\circ}\), the opposite side is \(y\) and the adjacent side is \(3\) m.
So, \(\tan30^{\circ}=\frac{y}{3}\)

Step2: Recall the value of \(\tan30^{\circ}\)

We know that \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\)

Step3: Solve for \(y\)

Substitute \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\) into \(\tan30^{\circ}=\frac{y}{3}\)

$$
LATEXBLOCK0
$$

Answer:

\(\sqrt{3}\) meters