Question

solving using trig ratios
determining which ratio to use:

1. circle the __________
2. label the sides that are marked in reference to that angle

• 3 possible pairings:
• _____ and ____
• _____ and ____
• _____ and ____

1. choose the correct function based on the pairing

$\sin = \frac{\quad}{hyp}$ \quad $\cos = \frac{\quad}{hyp}$ \quad $\tan = \frac{\quad}{adj}$

1. set-up and solve your equation for the missing side or angle

$\underline{\quad\quad\quad\quad\quad}$ (angle) $= \frac{\quad}{side}$

using sin:
(first triangle: right triangle, angle 29°, hypotenuse 34, opposite side x)
(second triangle: right triangle, angle 48°, hypotenuse x, adjacent side 24)
(third triangle: right triangle, hypotenuse 25, adjacent side 7, angle x°)

Explanation:

Step1: Identify the triangle and angle

We have a right - triangle with hypotenuse \(34\), angle \(29^{\circ}\), and the side opposite to the angle \(29^{\circ}\) is \(x\).

Step2: Recall the sine formula

The formula for sine of an angle in a right - triangle is \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 29^{\circ}\), opposite side \(=x\), and hypotenuse \( = 34\). So we set up the equation \(\sin(29^{\circ})=\frac{x}{34}\).

Step3: Solve for \(x\)

Multiply both sides of the equation \(\sin(29^{\circ})=\frac{x}{34}\) by \(34\) to get \(x = 34\times\sin(29^{\circ})\).
We know that \(\sin(29^{\circ})\approx0.4848\). Then \(x\approx34\times0.4848 = 16.4832\approx16.48\)

Answer:

\(x\approx16.48\)