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

1 Answer

Nov 20, 2015

The other two sides have lengths $\frac{7}{2}$ $7/2$ and $\frac{7 \sqrt{3}}{2}$ $(7sqrt(3))/2$

Explanation:

See image below: enter image source here
The specified values are in $black$ $color(black)("black")$

The standard length ratios of the sides of a $\frac{π}{3}$ $pi/3$ triangle are in $blue$ $color(blue)("blue")$

As can be seen from the hypotenuse the ratio $\frac{specified length}{standard length} = \frac{7}{2}$ $("specified length")/("standard length") = 7/2$

So the two non-specified sides have lengths

$XXX \frac{7}{2} \times 1 = \frac{7}{2}$ $color(white)("XXX")7/2xxcolor(blue)(1) = 7/2$
and
$XXX \frac{7}{2} \times \sqrt{3} = \frac{7 \sqrt{3}}{2}$ $color(white)("XXX")7/2xxcolor(blue)(sqrt(3)) = (7sqrt(3))/2$

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