Question

Find c in the pic below

Answer 1

A

Explanation:

To find the angle inside the triangle (to the right side of 90 degree angle), we first have to find the adjacent angle (below it).

Angle 122 and that adjacent angle is same (parallel lines cut by transversal -- they are corresponding angles).

So that angle is 122.

The inside triangle angle (what we want) is adjacent to 122, so we can write:

Angle + 122 = 180 [straight angle/straight line is 180 degrees]

Solving for that angle, we have:

Angle = 180 - 122 = 58

Now, looking at the triangle, Side C is "opposite" of 58° and side "20" is the side that is "hypotenuse" [side opposite of 90 degree angle is hypotenuse).

Which trig ratio relates "opposite" and "hypotenuse"??

Yes, it is SIN. Thus we can write:

`Sin(58)=(Opposite)/(Hypotenuse)=(C)/(20)`

We can now solve for C:

`Sin(58)=(C)/(20)\\C=20*Sin(58)\\C=16.96`

Correct answer is A