Question

Find the depth of the cut and round to the nearest hundredth as needed

Answer 1

We have a triangular cut, where its base measures 5.6in. Since the cut is symmetrical, the height of this triangle bissects the opposing angle to the base.

If we bissect the the angle opposing the base, we get the following right triangles

The tangent of an angle in a right triangle is given by the ratio between the opposite side of an angle and the adjacent side. Using this trigonometric relation, we have

`\sin (58.3^o)=(2.8)/(x)`

Solving for x, we have

`\begin{gathered} \sin (58.3^o)=(2.8)/(x) \\ x\sin (58.3^o)=2.8 \\ x=(2.8)/(\sin (58.3^o)) \\ x=3.29097724393\ldots\approx3.29 \end{gathered}`

The depth of the cut is 3.29 in.