We read your photo as:

For an inclined plane, the relationship between the height (h) to which a load is raised, the length of the inclined plane (L, which is the distance moved by the effort), and the angle of inclinat

Mathematics

ScanSolve AI Answer

Answer

A) 28.28 m\text{A) } 28.28 \text{ m}

Step-by-step solution

4 steps

For an inclined plane, the relationship between the height (hh) to which a load is raised, the length of the inclined plane (LL, which is the distance moved by the effort), and the angle of inclination (θ\theta) is given by the sine function:

sin⁡(θ)=oppositehypotenuse=hL\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{L}
  1. Identify the given values.

    • Angle of inclination, θ=45∘\theta = 45^\circ.
    • Height the load is moved, h=20 mh = 20 \text{ m}.
  2. Rearrange the formula to solve for the distance moved by the effort (LL).

    L=hsin⁡(θ)L = \frac{h}{\sin(\theta)}
  3. Substitute the given values into the formula.

    L=20 msin⁡(45∘)L = \frac{20 \text{ m}}{\sin(45^\circ)}

    We know that sin⁡(45∘)=22≈0.7071\sin(45^\circ) = \frac{\sqrt{2}}{2} \approx 0.7071.

    L=20 m0.7071L = \frac{20 \text{ m}}{0.7071} L≈28.284 mL \approx 28.284 \text{ m}
  4. Compare the calculated value with the given options.

    The calculated distance is approximately 28.28 m28.28 \text{ m}. This matches option (A).

    The final answer is A) 28.28 m\text{A) } 28.28 \text{ m}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question