Question

using trig functions and the given triangle, find the value of x and y to the nearest tenth.

x = select m
y = select m
(see yellow hint below.)

Explanation:

Step1: Find \(x\) using sine function

The sine of an angle in a right - triangle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the opposite side to the \(30^{\circ}\) angle is \(4\) m, and the hypotenuse is \(x\). So, \(\sin30^{\circ}=\frac{4}{x}\). Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{4}{x}\). Cross - multiplying gives \(x = 8.0\) m.

Step2: Find \(y\) using 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 \(4\) m, and the adjacent side is \(y\). So, \(\tan30^{\circ}=\frac{4}{y}\). Since \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\approx0.577\), we can solve for \(y\) as \(y=\frac{4}{\tan30^{\circ}}\). Substituting the value of \(\tan30^{\circ}\), we get \(y = 4\sqrt{3}\approx6.9\) m.

Answer:

\(x = 8.0\) m, \(y = 6.9\) m