Question

use the following diagram to answer question 5.

1. solve for ( x ) and ( y ) in the above triangle. round to one decimal place if needed.

step 1: solve for ( x ).
step 2: solve for ( y ).

Explanation:

Step1: Solve for \(x\)

Use the sine function in the right - triangle with hypotenuse \(93\) mm and angle \(19^{\circ}\).
The formula for sine is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
Here, \(\theta = 19^{\circ}\), the opposite side is \(x\) and the hypotenuse is \(93\) mm.
So, \(x = 93\times\sin(19^{\circ})\).
Using a calculator, \(\sin(19^{\circ})\approx0.3256\).
Then \(x=93\times0.3256 = 30.3\) mm (rounded to one decimal place).

Step2: Solve for \(y\)

Use the sine function in the right - triangle with opposite side \(x = 30.3\) mm and angle \(55^{\circ}\).
The formula \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\) gives \(y=\frac{x}{\sin(55^{\circ})}\).
Since \(x = 30.3\) mm and \(\sin(55^{\circ})\approx0.8192\).
Then \(y=\frac{30.3}{0.8192}\approx37.0\) mm (rounded to one decimal place).

Answer:

\(x = 30.3\) mm, \(y = 37.0\) mm