Jane decides to build a wooden pencil box. She allows 32cm along the diagonal. The width of the box is to be 8cm. find the angle that the diagonal makes with the length of the box.
To find the angle that the diagonal makes with the length of the box, we can use trigonometry.
Let's start by visualizing the situation. We have a right triangle formed by the length, width, and diagonal of the pencil box.
The length of the box represents one of the legs of the right triangle, the width represents the other leg, and the diagonal represents the hypotenuse.
We know the width of the box is 8cm, and the diagonal measures 32cm. We need to find the angle that the diagonal makes with the length.
To solve this, we can use the inverse trigonometric function, specifically the inverse sine function (sin⁻¹), which will enable us to find the angle.
Using the formula for sine (sinθ = opposite/hypotenuse), we have sinθ = width/diagonal.
Substituting the given values, we get sinθ = 8cm/32cm.
Now, we can calculate the value of sinθ using a calculator or by dividing 8 by 32, which gives us 0.25.
Next, we need to find the inverse sine (sin⁻¹) of 0.25 to find the angle.
Using a calculator, we can input sin⁻¹(0.25) and get the result approximately equal to 14.478°.
Therefore, the angle that the diagonal makes with the length of the box is approximately 14.478°.