(Find the length of the missing side in each triangle)

9514 1404 393

  see attached

Step-by-step explanation:

The relevant trig relations are summarized by the mnemonic SOH CAH TOA. This means ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

So, for each triangle, determine the relationships of the given sides to the given angle: adjacent, opposite, or hypotenuse. Then write and solve the equation using one of the above templates.

First of all let's rearrange the equation for the given line:

4x + 7y + 3 = 0
7y = -4x - 3
y = (-4/7)x - 3/7
Now we know that the gradient of the line is -4/7

The gradients of two perpendicular lines multiply by each other to give -1, ie.
(-4/7)*m = -1
m = -1/(-4/7)
= 7/4, therefor the gradient of the perpendicular line is 7/4

Now we can substitute this and the point (-2, 1) into the equation y - y1 = m(x - x1)
y - 1 = 7/4(x - (-2))
y = 7/4x + 7/2 + 1
y = 7/4x + 9/2

If we look at the given answers then C is correct, since 9/2 = 18/4 and so the equation may also be written as y = 7/4x + 18/4