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

Answer:

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

Explanation:

See image below:enter image source here
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#