Question

If you're good at trigonometry please help meeee

On a 30-60 set square, the side opposite the 60 degree angle is 80mm long. Find the length of the longest side to the nearest millimetre

Answer 1

`\boxed{92 \: \mathrm{mm}}`

Explanation:

sin θ =
`(opposite)/(hypotenuse)`

sin (60) =
`(80)/(x)`

x =
`\frac{80}{\mathrm{sin} (60)}`

x = 92.37604307...

x ≈ 92

Answer 2

Using the base dimension and either given angle you can solve for x

Sin(angle) = opposite leg/ hypotenuse

Sin(60) = 80/x

X = 80/sin(60)

X = 80/ sqrt(3)/2

X = 160/3 x sqrt(3). (This is exact answer)

For a decimal answer: 160/3 = 53 1/3

Multiplied by sqrt(3) = 92.376 mm

Rounded to nearest mm = 92