Answer:
x = 12.45
Step-by-step explanation:
For this triangle, let's use the SOH CAH TOA method to solve for x.
For easier visualization, rotate the triangle 90 degrees to the left.
To solve for x, we have to use the CAH from SOHCAHTOA. This is because cos(theta) = adjacent / hypotenuse. The adjacent side of the angle is 7 and the hypotenuse is x.
Now that we have this setup: cos(65) = 7/x, let's isolate x. In order to do that, multiply both sides by x and divide both sides by cos(65). That'll give us 7/cos(65) = x. We are in need of a calculator to find cos(65).
cos(65) is -0.562 approximately. Divide 7 by this and you'll get -12.45 rounded to the nearest hundredth, approximately.
Now, before we go, why the negative? Does it make sense, here? Let's only look at the line that x forms. It "starts" from the left and goes to the right. The slope is essentially negative. (Because the x-value is negative and the y-value is positive if this triangle were to be on a quadrant plane). So, yes, visually, it makes sense.
