Question 309300: Hello, I'm sorry if this question is confusing but i don't understand this, so it's sort of hard to explain. Okay, i have triangle ABC. Angle ABC=90 Degrees, Angle BCA=75 Degrees, and angle CAB=15 Degrees. If the length of line BC equals 20 units, what is the length of line AB? Please explain.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! If you draw the triangle and label it's parts, you'll see that triangle ABC is a right triangle. Now let's use angle BCA=75 degrees as our reference angle. The side BC is the adjacent side while the side AB is the opposite side (again, a drawing will help). So we're going to use the tangent function (since tan=opposite/adjacent)
So this means that tan(75)=BC/AB and that tan(75)=20/x where 'x' is the length of AB. Now compute tan(75) to get approximately 3.73205. So 3.73205=20/x
Now you're job is to solve the equation 3.73205=20/x to find 'x' which is the length of AB.
Note: There is a way to compute the tangent of 75 degrees exactly, but we don't need to do that here.
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