# Trig help

#### sinjid9

The perimeter of a triangle is 100cm and the angles are in the ratio of 1:3:5. Find the length of each side.

#### bigwave

first get the angles

divide $$\displaystyle 180^o$$ by $$\displaystyle 9$$ then apply the ratio's to get the $$\displaystyle 3$$ angles

so

$$\displaystyle 20^o(1) = 20^o$$
$$\displaystyle 20^o(3) = 60^o$$
$$\displaystyle 20^o(5) = 100^o$$

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#### sinjid9

Yeah I had already gotten that but what am I supposed to do with those values?

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#### bigwave

one possible way to get the length of the sides is to temporarily give one of the sides a length of 1 then find the lengths of the other sides by the law of sines in proportion to that then you will have another ratio to apply to the 100cm perimeter.

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sinjid9

#### 11rdc11

The perimeter of a triangle is 100cm and the angles are in the ratio of 1:3:5. Find the length of each side.
$$\displaystyle x+3x+5x= 180$$

$$\displaystyle x = 20$$

angles are 20,60,100

Now use these formulas

$$\displaystyle \frac{\sin{60}}{a} = \frac{\sin{20}}{b} = \frac{\sin{100}}{c}$$

$$\displaystyle a + b + c = 100$$

Now solve for a variable and sub

$$\displaystyle a = \frac{b\sin{60}}{\sin{20}}$$

$$\displaystyle c = \frac{b\sin{100}}{\sin{20}}$$

so now sub

$$\displaystyle \frac{b\sin{60}}{\sin{20}} + b + \frac{b\sin{100}}{\sin{20}} = 100$$

sinjid9

#### sinjid9

one possible way to get the length of the sides is to temporarily give one of the sides a length of 1 then find the lengths of the other sides by the law of sines
I only understood up to that part.

#### bigwave

as mentioned you should get

approximately:

15.6 + 44.9 + 39.5 = 100