Question: Trigonometry Quiz
x°
49
38
X = __________ degrees (in 2 sig figs)
A right triangle is shown in the center-left of the page: the left side is vertical, the bottom side is horizontal labeled 38, and the slanted hypotenuse is labeled 49; the angle x° is at the bottom-right vertex.
1. **State the problem:** We need to find the angle $x^\circ$ in a right triangle where the adjacent side to $x$ is $38$ and the hypotenuse is $49$.
2. **Formula used:** In a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse:
$$\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}}$$
3. **Apply the formula:**
$$\cos(x) = \frac{38}{49}$$
4. **Calculate the ratio:**
$$\frac{38}{49} \approx 0.7755$$
5. **Find the angle $x$ by taking the inverse cosine:**
$$x = \cos^{-1}(0.7755)$$
6. **Calculate $x$ using a calculator:**
$$x \approx 39.2^\circ$$
7. **Round to 2 significant figures:**
$$x \approx 39^\circ$$
**Final answer:**
$$x = 39^\circ$$