SOLUTION: i am trying to figure out the lengths of the sides of a triangle i have the height and the angle but nothing else. overall height is 4 feet angles are 60 deg. 60

Question 706295: i am trying to figure out the lengths of the sides of a triangle i have the height
and the angle but nothing else.
overall height is 4 feet
angles are 60 deg.
60 deg.
60 deg.
how do i figure out?
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
i am trying to figure out the lengths of the sides of a triangle i have the height
and the angle but nothing else.
overall height is 4 feet
angles are 60 deg.
60 deg.
60 deg.
-----
Sketch an equilateral triangle with each side = 2s.
---
Draw an altitutde from one of the sides to the opposite vertex.
---
That altitude is a perpendicular bisector of the base.
----
Each piece of that base is "s".
----
Now use Pythagoras to solve for "2s".
base = s
altitude = 4
hypotenuse = side of the triangle = 2s
-----------------------------
(2s)^2 = s^2 + 4^2
4s^2 = s^2 + 16
3s^2 = 16
s^2 = 16/3
s = 4sqrt(3)/3
----
side = 2s = (8/3)sqrt(3)
============================
Cheers,
Stan H.
===================

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The other poster solved it for you, but I figured I'd draw out a pic for you so you can see what's going on.

Start with an equilateral triangle (note an equilateral triangle has three 60 degree angles, ie all angles are equal, and all sides are equal)

So let x = side length of equilateral triangle

We would get this pic if we drew out an equilateral triangle

Now cut the triangle in half. Pick any vertex and draw a perpendicular line to the opposite side. I'm going to pick the top vertex to get this

Note: the opposite side is cut in half, so the bottom side of x gets cut in half to get two equal pieces of

Another Note: the top angle gets cut in half to get two equal 30 degree angles

So we have a 30-60-90 triangle with legs: and , the hypotenuse is units

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