Question

A builder is constructing a roof. The wood for the sloped section
of the roof is 5 m long and the peak of the roof need to be 3 m.
What angle should the piece of wood make with the base of the
roof?

Answer 1

To find the angle that the piece of wood makes with the base of the roof, we can use some basic trigonometry.

In this case, we have a right triangle where:
- The length of the wood (the hypotenuse) is 5 m,
- The height (the vertical leg from the base to the peak) is 3 m,
- The base (the horizontal leg) is what we need to find out.

We can use the sine function, which is defined as:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Here, the opposite side is the height of the roof (3 m), and the hypotenuse is the length of the wood (5 m):

\[
\sin(\theta) = \frac{3}{5}
\]

Now we can find the angle \(\theta\) by taking the inverse sine (arcsin):

\[
\theta = \arcsin\left(\frac{3}{5}\right)
\]

Calculating this gives:

\[
\theta \approx 36.87^\circ
\]

Thus, the angle that the piece of wood should make with the base of the roof is approximately \(36.87^\circ\).