Verified answer

EASIEST WAY OF FINDING ANGLES:

Remember that the total degrees possible in a triangle is 180 degrees- so if you have 2 angles of ANY triangle, then if you subtract those from 180 degrees you can find the missing angle:

ie, if a triangle has angles a, b and c:

A

......|\......

......| \......

......| \......

......|___\......

....C........B......

If A= 30 degrees, and C = 90 degrees

then to find B:

180 (total) = 30 (A) + ? (B) + 90 (C)

180 - 30 - 90 = B

B = 60

More complex stuff (if necessary)

For Right-Angled Triangles:

If you need to find 1 missing length of a triangle:

Pythagorean Theorem : a^2 + b^2 = c^2

where a and b are the "legs" of the triangle (the shorter bits) and c is the longest side/the diagonal one (called the hypotenuse). Basically, if you need to find what one of the sides are, you plug in the other two sides in the equation above, and then solve it to find the missing side.

If you need to find MORE than 1 missing side or angle:

You can use one of 3 of the trigonometric ratios:

Here is my awesomely made triangle diagram! (I feel smart now!)

A

......|\......

......| \......

..o..| \....h

......|___\......

....C...a....B

o/h -> the opposite side divided by the hypotenuse will give you the angle of the adjacent side (angle A)

a/h -> the adjacent side length divided by the hypotenuse will give you the angle of the opposite side (angle B)

o/a -> the opposite side divided by the adjacent side to give you the hypotenuse angle (angle C)

You can also use all this to find the lengths of sides- for example, the o angle (B) divided by the h angle (C) will give you the a angle (A)