Answer:
A. 5/√89
Explanation:
Before I explain the answer, I want to point out that finding the length of AC isn't necessary. I will explain this in a little bit.
Angle AEB is part of the triangle AEB. We know that one of its angles, ABE, is 90 degrees. We also know that the sum of every triangle's total angles is 180 degrees. Upon further investigation, you can see that you can solve for angle BAE with the given lengths of CD and AD. In order to know this, you need to know S(o/h)C(a/h)T(o/a). With the angle being BAE, CD and AD would be the opposite and adjacent sides, respectively. This means we will use T(o/a), which means tanθ =o/a. (Now going back to why finding the length of AC isn't necessary- finding an angle needs only one of S(o/h)C(a/h)T(o/a), if we already have the needed values for one of them, we don't need to take an unnecessary step to find the extra value.)
Anyway, to isolate θ in the equation tanθ=o/a, we take the inverse tan of o/a. This might sound confusing, but basically, using the inverse of tan is basically like multiplying both sides by tan to cancel it on one side. Inverse tan looks like this: tan^-1, tan to the power of negative 1.
Plug in 5 (opposite) and 8 (adjacent) into our equation.
<em>tanθ=o/a</em>
<em>tanθ=5/8</em>
<em>θ=tan^1(5/8)</em>
<em>θ=32.00538321</em>
Now we know angle BAE is 32 degrees. Now add it to the angle ABE and subject the sum from 180.
<em>32.00538321+90=122.0053832</em>
<em>180-122.0053832=57.99461679</em>
Angle AEB is 57.99461679 degrees. Now all we have to do is find cos(57.99461679).
<em>cos(57.99461679)=0.52999894</em>
For choice A, 5 divided by √89 is also 0.52999894, therefore it is correct.
