Question

Right angled triangle with hyp length 7 contains the angle pi/3. What is exact lengths of the other two sides?

Answer 1

The other two sides have lengths `7/2` and `(7sqrt(3))/2`

Explanation:

See image below:
The specified values are in `color(black)("black")`

The standard length ratios of the sides of a `pi/3` triangle are in `color(blue)("blue")`

As can be seen from the hypotenuse the ratio `("specified length")/("standard length") = 7/2`

So the two non-specified sides have lengths

`color(white)("XXX")7/2xxcolor(blue)(1) = 7/2`
and
`color(white)("XXX")7/2xxcolor(blue)(sqrt(3)) = (7sqrt(3))/2`