Subjects trigonometry

Ramp Height E7Fd15

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We have a ramp that is 60 feet long and makes a 15° angle with the ground. We want to find the height of the second floor above the first floor, which corresponds to the vertical leg of the right triangle formed. 2. **Formula used:** In a right triangle, the height (opposite side) can be found using the sine function: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ where $\theta$ is the angle with the ground. 3. **Apply the formula:** $$\sin(15^\circ) = \frac{\text{height}}{60}$$ 4. **Solve for height:** $$\text{height} = 60 \times \sin(15^\circ)$$ 5. **Calculate sine value:** $$\sin(15^\circ) \approx 0.2588$$ 6. **Find height:** $$\text{height} = 60 \times 0.2588 = 15.528$$ 7. **Round to nearest tenth:** $$15.5$$ feet **Final answer:** The second floor is approximately 15.5 feet above the first floor.