Question 624357
Since we started with a rectangle, the "resulting piece" is a right triangle with legs of 4 and 8 feet. TO find the acute angles in this right triangle we will use the two sides we know and an Trig function wthat would have those two sides in its ratio.<br>
Let's start with the angle that has the 8 ft side. Let's call this angle A. From the point of view of angle A, the 8 ft side is the adjacent side and the 4 ft side is the opposite side. Which Trig functions have opposite and adjacent in their ratios? Answer: tan and cot. And since our calculator probably does not have a button for cot, we will use tan.<br>
Since tan is opposite over adjacent the equation we will use is:
{{{tan(A) = 4/8 = 1/2}}}
So A is the acute angle whose tan is 1/2. For this we use the inverse tan button, {{{tan^(-1)(x)}}}, button:
Making sure the calculator is working in degree mode and entering:
{{{tan^(-1)(1/2)}}}
You should get A = 26.56505118<br>
For the other angle, let's call it B, we can use
{{{tan(B) = 8/4}}}
Or we could just use the fact that the three angle must add up to 180:
B = 180 - 90 - 26.56505118
Either way we should get B = 63.43494882