To determine how far above the ground the top of the slide is, we can use trigonometry. Specifically, we will use the sine function, which relates the angle of a right triangle to the ratio of the length of the opposite side to the hypotenuse.
Here’s the step-by-step solution:
1. Visualize the Right Triangle:
- The length of the slide is the hypotenuse of the right triangle.
- The height above the ground is the side opposite the given angle (35 degrees).
- The base is the distance along the ground from the start to the base of the slide.
2. Use the Sine Function:
- The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse.
- In this case, we are dealing with angle [tex]\( \theta = 35^{\circ} \)[/tex], hypotenuse [tex]\( h = 4.1 \)[/tex] meters, and we want to find the opposite side [tex]\( O \)[/tex].
[tex]\[
\sin(\theta) = \frac{O}{h}
\][/tex]
3. Substitute the Known Values and Solve for [tex]\( O \)[/tex]:
[tex]\[
\sin(35^{\circ}) = \frac{O}{4.1}
\][/tex]
Multiplying both sides by 4.1 to isolate [tex]\( O \)[/tex]:
[tex]\[
O = 4.1 \times \sin(35^{\circ})
\][/tex]
4. Calculate the Value:
- Using the sine function, [tex]\( \sin(35^{\circ}) \)[/tex] is approximately 0.5736.
[tex]\[
O = 4.1 \times 0.5736 \approx 2.3517 \text{ meters}
\][/tex]
5. Round to the Nearest Tenth:
- The calculated height is approximately 2.3517 meters.
- When rounded to the nearest tenth, this value becomes 2.4 meters.
Therefore, to the nearest tenth of a meter, the top of the slide is 2.4 meters above the ground.
Among the given choices:
- 5.0 m
- 3.4 m
- 2.4 m
The correct answer is 2.4 m.
