4100.21 – Find a Sine

Tags:Problem Set 15Algebra/TrigonometryTrigonometry

Find a formula for sin A, in terms of b and c only. (N.B. it's an isosceles triangle)

Solution

Sin A = hc\frac{h}{c}.

h=c2−(b2)2h = \sqrt{{c^2}-(\frac{b}{2})^2} = c2−b24\sqrt{{c^2}-\frac{{b^2}}{4}} = 4c2−b24\sqrt{\frac{4c^2-b^2}{4}} = 4c2−b22\frac{\sqrt{4c^2-b^2}}{2}.

So sin A = 4c2−b22c\frac{\sqrt{4c^2-b^2}}{2c}