SOLUTION: Hi, i'm having a bit of trouble do you think you could help? the angles of a triangle are in the ratio 3:4:5. If the shortest side has a length of 1 meter, what idsthe length

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Question 168863: Hi,
i'm having a bit of trouble do you think you could help?
the angles of a triangle are in the ratio 3:4:5. If the shortest side has a length of 1 meter, what idsthe length of the longest side?
thanks!
=)

Answer by jojo14344(1513)   (Show Source): You can put this solution on YOUR website!
.
To begin with, 1st we need to find the ANGLES of the triangle.
Given Ratio ----> 3:4:5 ------>
Agree? Divide All Angles by 15: ;;
.
Let's put those angles in figure so it will be easy to analyze:
---> As you see in our drawing,
is the shortest side = 1meter.
For argument sake, take a protractor and
draw on your own to have the right angles and measure the shortest.
.
Here's the trick, determining the longset side because it seems the other 2 sides are so close. Draw a Line from to Line and mark point :

.
We can solve for Line by Pyth Theorem --> -->
---------> EQN 1
*note: , and we need to find ?
By trigo function: ---> --> , Plug in EQN 1:


.
Now we need to find . By Trigo function,

.
So, line
.
Now,we find Line . We can do that either by Trigo Function or Cosine Law. Let's try both and we'll see if the same.
By Trigo function--->

Or By Cosine Law --->


, The same above
.
So here are your measurements:
----------> Longest
-------------------------> Shortest
--------------------> Middle

.
Thank you,
Jojo

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