What angle does the board need to be cut at?

Question

If someone has a 2'' wide board and a 1 1/2'' wide board, and they want to cut the narrower board at an angle so the cut is 2'' long and the boards will fit together, what angle do they need to cut the board?

Here is what I've come up with so far. cos (angle) = adj / hypotenuse cos (angle)= 1.5 / 2 cos-1 (0.75) = 41.40962211 degrees

I am not familiar with the functions sin, cos, or tan just yet, so my apologies if my work is confusing. Thanks in advance!

Answer 1

The animation makes it obvious that $$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{1.5}{2} = \frac{3}{4},$$ consequently $$\theta = \sin^{-1} \frac{3}{4} \approx 0.848062 \, \text{radians} \approx 48.5904^\circ.$$

Answer 2

The piece you remove will be a right angled triangle with

a hypotenuse of $2$ and

one side of length $\frac 32$

you must cut at angle of

$$ \theta = \cos^{-1}( \frac 34 ) \approx 41.41^o $$