Sarah's Blog

Week 17 – Sine Law

The sine law can be used for any triangle to determine the length of a side or to find an angle.

The formula can be used in this form, \frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C} or this form, \frac{Sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}

When the variable is in the numerator, it is easier to solve for it. To find the side length, use the first formula. Two angles and the length of one of the sides must be known.

To find an angle, use the second one. Two side lengths and one angle must be known.

Finding the side length:

Use \frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}

Plug in the given values.

\frac{a}{sin 75} = \frac{b}{sin B} = \frac{12.50}{sin 35}

Since we don’t know anything in the fraction \frac{b}{sin B}, we don’t use it.

So, \frac{a}{sin 75} = \frac{12.50}{sin 35}

Solve for a: a = \frac{12.50(sin 75)}{sin 35}

The side length of a = 21.05 cm

Finding an angle:

Use \frac{Sin P}{p} = \frac{sin Q}{q} = \frac{sin R}{r}

Plug in the given values.

\frac{Sin P}{p} = \frac{sin 65}{8.6} = \frac{sin R}{6.1},

Use \frac{sin 65}{8.6} = \frac{sin R}{6.1}

Solve.

sarahl22015 • June 13, 2018

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