Geometry: Coordinates and Angles

Worked Solution

We can use the following formula to find angle H:

Cosine Rule: h2 = k2 + g2 – 2 kg cos(H)  or  cos(H) =

k2 + g2 – h2 2 kg

First we will need the lengths of the sides g, h and k.
As we are given the coordinates of GHK we can use Pythagoras' Theorem to find these lengths
but we also need their squares in the Cosine Rule:
g² = (9 – 3)² + (0 – 0)² = 36 so g = √36 = 6
h² = (9 – (–5))² + (0 – (–8))² = 260
k² = (3 – (–5))² + (0 – (–8))² = 128 so k = √128 = 11.31371

Substituting these in the formula for cos(H) we have:

128 + 36 – 260 2 √128 √36

= –0.70711

Angle H = arccos( –0.70711) = 135°