Work out the area of a triangle using sin
What's the sin rule?
Area = ½ ab Sinθ
Where a and b are the lengths of the sides we know, and θ the angle between them.
What do we use it for?
The basic formula for finding the area of a triangle is A = ½ x base x height
But sometimes you don’t know the height of the triangle, in fact, in real life it’s very rare that someone would know the ‘perpendicular height’ of any triangle they had to use.
We can use this formula to work out the area when we don't know the height.
When do we use it?
When we know the length of two sides, and the angle in between them.
Note! It’s very similar to the first formula you learnt, in fact almost identical. You’re still multiplying two numbers together, and then halving them. Adding Sin θ to the end is a trick to turn one of the sides into the ‘perpendicular height’.
In real life, this is far more useful than the older formula, since anyone who needs to use geometry in their work is likely to know the lengths of the sides of any triangles they are working with.
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