Question

1. find the missing side. round to the nearest tenth. 7.1 7.0 6.8 6.9

Explanation:

Step1: Identify trigonometric ratio

The triangle is right-angled, with hypotenuse 10 and angle 35°. The side x is opposite the 35° angle. Use sine: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Set up equation

$\sin(35^\circ) = \frac{x}{10}$

Step3: Solve for x

$x = 10 \times \sin(35^\circ)$

Step4: Calculate value

$\sin(35^\circ) \approx 0.5736$, so $x \approx 10 \times 0.5736 = 5.736$ (Note: If the angle was adjacent, cosine would be used, but based on standard labeling, opposite is correct. Wait, if x is adjacent, $\cos(35^\circ) = x/10$, $x≈10×0.8192≈8.192$. But the options are 6.8-7.1. Wait, maybe x is adjacent? Wait, no, let's check again. Wait, maybe the angle is at the other end. Wait, the options are 6.8-7.1. Let's use tangent: if x is opposite, angle 35°, adjacent side? Wait, no, the hypotenuse is 10. Wait, maybe the angle is 35°, hypotenuse 10, x is opposite: 5.7, not in options. If x is adjacent: 8.2, not in options. Wait, maybe the side labeled 10 is adjacent? Then $\tan(35^\circ)=x/10$, $x≈10×0.7002≈7.0$. Oh! Maybe I misidentified the sides. If the angle 35° has adjacent side 10, then opposite side x: $\tan(35°)=x/10$, so x=10×tan(35°)≈10×0.7002≈7.0. That's option B.

Step5: Correct side identification

Assume 10 is adjacent to 35°, x is opposite. Use tangent: $x=10×tan(35°)≈7.0$

Final Answer:

7.0

Answer:

6.1