Question: Find the length of the unknown side correct to one decimal place.
A
65°
17 m
B
x
C
18.8 m
15.4 m
7.2 m
7.9 m
Graph shape: a right triangle in the top-left/center area, with angle A = 65° at the top-left vertex, right angle at B on the lower-left vertex, hypotenuse AC labeled 17 m, and base BC labeled x; the unknown side x is the bottom side from B to C.
1. **State the problem:** We have a right triangle ABC with a right angle at B, angle $A = 65^\circ$, hypotenuse $AC = 17$ m, and we want to find the length of side $BC = x$.
2. **Recall the trigonometric relationship:** In a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse.
$$\cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{BC}{AC}$$
3. **Apply the formula:**
$$\cos(65^\circ) = \frac{x}{17}$$
4. **Solve for $x$:**
$$x = 17 \times \cos(65^\circ)$$
5. **Calculate the cosine value:**
$$\cos(65^\circ) \approx 0.4226$$
6. **Calculate $x$:**
$$x = 17 \times 0.4226 = 7.1842$$
7. **Round to one decimal place:**
$$x \approx 7.2$$
**Final answer:** The length of side $BC$ is approximately $7.2$ meters.