Question

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

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

Explanation:

Step1: Use trigonometric ratios

For a right - angled triangle with an angle of \(45^{\circ}\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, hypotenuse \(c = 22\) mm, \(\theta=45^{\circ}\), \(x\) is the adjacent side and \(y\) is the opposite side.
Since \(\sin45^{\circ}=\frac{y}{22}\) and \(\cos45^{\circ}=\frac{x}{22}\), and \(\sin45^{\circ}=\cos45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707\)

Step2: Calculate \(x\) and \(y\)

For \(x\): \(x = 22\times\cos45^{\circ}\)
\(x=22\times\frac{\sqrt{2}}{2}=11\sqrt{2}\approx11\times1.414 = 15.6\)
For \(y\): \(y = 22\times\sin45^{\circ}\)
\(y=22\times\frac{\sqrt{2}}{2}=11\sqrt{2}\approx11\times1.414 = 15.6\)

Answer:

\(x = 15.6\) mm, \(y = 15.6\) mm