Math Is Fun Forum

lisathedork

Member

Registered: 2013-10-24

Posts: 36

Special Right Triangles

May I please get some tips on how to do this? I thought I would get this but I'm having some trouble but thank you!

If you have a 45-45-90 triangle:

2. With a hypotenuse of SQRT(6), what is the length of one leg?

6. And one leg has a length of SQRT(8), what is the length of the hypotenuse?

7. And one leg has a length of SQRT(32), what is the length of the hypotenuse?

If you have a 30-60-90 triangle:

13. And the length of the longest leg is 5[SQRT(3)], what's the length of the other leg?
14. Working from #13, what's the length of the hypotenuse?
15. And the length of the longest leg is 9, what is the length of shortest leg?
16. Working from #15, what is the length of the hypotenuse?
17. With a hypotenuse of 2[SQRT(3)] what is the length of the longest leg?
18. Working from #17, what is the length of the shortest leg?
19. And the length of the shortest leg is SQRT(12), what is the length of the longest leg?
20. Working from #19, what is the length of the hypotenuse?

Then I need help with Geometric Probability after. Before I post the questions may I please get some practice questions? Thanks again!!!

Last edited by lisathedork (2015-09-03 02:14:17)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Special Right Triangles

hi Lisa,

With 2, 6 and 7 you need more information.  There are many possible answers when you only know one side and a 90 angle.  Perhaps you were told something more in question 1.

In a 30-60-90 triangle:

Suppose you start with an equilateral triangle sides all 2s.  Cut the triangle in half so that the distance to the middle is s.  Rub out one half so all you have is a 30-60-90 triangle.

The hypotenuse is 2s, and the base is s.  Use Pythagoras:  height =  √ (2s.2s - s.s) =  √ (4s^2 - s^2) =  √ (3s^2) =  √ 3.s

So, for example in Q13, you are told the longest leg (height?) = 5 √ 3 so s=5.  The base is therefore 5 and the hypotenuse is 2x5.

Post back with more information for the earlier ones and I'll help with those.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

lisathedork

Member

Registered: 2013-10-24

Posts: 36

Re: Special Right Triangles

The help is no longer needed. I already figure the problems out, but thank you for the helpful information!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Special Right Triangles

hi Lisa,

I'm glad you sorted them out. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob