Math Is Fun Forum

demha

Member

Registered: 2012-11-25

Posts: 195

Special Right Triangles

I'm not understanding too well. I would really appreciate an explanation. I answered what I could (which isn't much at all). All the ones I did not answer, I would really appreciate an explanation as to how to solve them.

If you have a 45-45-90 triangle:

1. And the length of one leg is 3, what is the length of the other leg? - Answer: A
A 3
B 6
C9
D12
E 15
F 18

2. With a hypotenuse of SQRT(6), what is the length of one leg?
A sqrt 81
Bsqrt 3
Csqrt 12
Dsqrt 23
E sqrt 37
F sqrt 42

3. And one leg has a length of 5, what is the length of the hypotenuse? - Answer: F
A 2sqrt3
B6sqrt4
C7sqrt9
D9sqrt7
E 4sqrt5
F 5sqrt2

4. With a hypotenuse of 7[SQRT(2)], what is the length of one leg? - Answer: 7
A 12
B94
C22   
D7
E 45
F 2

5. With a hypotenuse of 6[SQRT(6)], what is the length of one leg?
A 6 sqrt(3) or 10.3923   
B4 sqrt(10) or 9.3156
C3 sqrt(4) or 2.5631
D1 sqrt(5) or 3.5941
E 2 sqrt(9) or 8.2145
F 8 sqrt(7) or 6.2211

6. And one leg has a length of SQRT(8), what is the length of the hypotenuse?
A 12
B9
C4
D18
E 26
F 2

7. And one leg has a length of SQRT(32), what is the length of the hypotenuse?
A 24
B8
C46
D12
E 65
F 34

8. With a hypotenuse of SQRT(3), what is the length of one leg?
A 1.225
B2.189
C7.641
D1.218
E 4.321
F 1.657

9. With a hypotenuse of 6, what is the length of one leg?

A 11sqrt3
B4sqrt7
C7sqrt8
D3sqrt2
E 8sqrt9
F 2sqrt5

10. And one leg has a length of 7[SQRT(72)] what is the length of the hypotenuse?
A 04
B48
C91
D84
E 75
F 23

If you have a 30-60-90 triangle:

11. And the length of the shortest leg is 4, what's the length of the hypotenuse? - Answer: 8
A 5
B12
C20
D52
E 8
F 4

12. Working from #11, what's the length of the other leg? - Answer: 6 (i understand that is is 4(square root 3), 4 x 4 = 16, 16 x 3 = 48 then square root this to get the answer. is my method correct?)
A 3.0713
B4.1579
C9.2357
D6.9282
E 10.084
F 9.1157

13. And the length of the longest leg is 5[SQRT(3)], what's the length of the other leg? - Answer: E
A 2
B7
C16
D27
E 5
F 24

14. Working from #13, what's the length of the hypotenuse? - Answer: A
A 10
B24
C57
D91
E 39
F 46

15. And the length of the longest leg is 9, what is the length of shortest leg?
A 6sqrt5
B9sqrt2
C5sqrt6
D7sqrt5
E 4sqrt2
F 3sqrt3

16. Working from #15, what is the length of the hypotenuse?
A 2sqrt5
B3sqrt4
C8sqrt9
D6sqrt3
E 10sqrt2
F 7sqrt4

17. With a hypotenuse of 2[SQRT(3)] what is the length of the longest leg?
A 7
B33
C9
D27
E 3
F 14

18. Working from #17, what is the length of the shortest leg?
A 1.7321
B1.9443
C1.8459
D1.2946
E 1.0906
F 1.6504

19. And the length of the shortest leg is SQRT(12), what is the length of the longest leg?
A 29
B6
C38
D56
E 61
F 17

20. Working from #19, what is the length of the hypotenuse?
A 8.4197
B1.9764
C10.5742
D6.2414
E 2.4971
F 6.9282

---

"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Special Right Triangles

hi demha,

Let's start with 1-5.  After that you may be able to tackle some more yourself.

If you have a 45-45-90 triangle:

1. And the length of one leg is 3, what is the length of the other leg? - Answer: A    correct 
A 3
B 6
C9
D12
E 15
F 18

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

hyp squared = 6  I think it is intended that the triangle is 45/45/90 again.  So the squares of these two added up must come to 6.  So 3 each.  But now square root to get the length of a side (leg).   

A sqrt 81
Bsqrt 3
Csqrt 12
Dsqrt 23
E sqrt 37
F sqrt 42

3. And one leg has a length of 5, what is the length of the hypotenuse? - Answer: F    correct
A 2sqrt3
B6sqrt4
C7sqrt9
D9sqrt7
E 4sqrt5
F 5sqrt2

4. With a hypotenuse of 7[SQRT(2)], what is the length of one leg? - Answer: 7   correct 
A 12
B94
C22   
D7
E 45
F 2

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

   hyp squared = 216.  Split in two = 108.  Now square root that for one leg.

A 6 sqrt(3) or 10.3923   
B4 sqrt(10) or 9.3156
C3 sqrt(4) or 2.5631
D1 sqrt(5) or 3.5941
E 2 sqrt(9) or 8.2145
F 8 sqrt(7) or 6.2211

post back if you can do 2 and 5 and see if you can do any others or ask for more hints.

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

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Special Right Triangles

2.
The answer is going to be sqrt 3 I believe.

---

5.
6[SQRT(6)]
6 x 6 x 6 x 6 x 6 x 6 = 46656
(after squaring) 216
Cut in half for 108.
(after squaring) 10.3923

ANSWER: A - 6 sqrt(3) or 10.3923

Last edited by demha (2013-07-23 11:39:13)

---

"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Special Right Triangles

Both correct, well done!

6. And one leg has a length of SQRT(8), what is the length of the hypotenuse?   Square this; double it and square root.
A 12
B9
C4
D18
E 26
F 2

7. And one leg has a length of SQRT(32), what is the length of the hypotenuse? same method 
A 24
B8
C46
D12
E 65
F 34

8. With a hypotenuse of SQRT(3), what is the length of one leg? You have now done questions like this. 
A 1.225
B2.189
C7.641
D1.218
E 4.321
F 1.657

9. With a hypotenuse of 6, what is the length of one leg?    ditto

A 11sqrt3
B4sqrt7
C7sqrt8
D3sqrt2
E 8sqrt9
F 2sqrt5

10. And one leg has a length of 7[SQRT(72)] what is the length of the hypotenuse?   and again
A 04
B48
C91
D84
E 75
F 23

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

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Special Right Triangles

Let me just do #6 to see if I got it right:
SQRT(8)
8 x 8 = 64
62 x 2 = 128
square 128 for 11.313 and round off to nearest number which will be A: 12. | Is this the correct way?

----
#10:
7sqrt(72) x 2 = 7(sqrt144).
7(sqrt144) = 7(12) = 7 x 12 = 84

Answer is 84... correct?

Last edited by demha (2013-07-24 02:32:13)

---

"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Special Right Triangles

Alright I think I got the rest of them!
#6.
Answer is C: 4

#7.
Answer is B: 8

#8.
Now here is how I did this, tell me if I'm wrong/right:
SQRT(3) divided by 2 = SQRT1.5.
after squaring I get 1.224. Do I round off to the nearest which is answer A: 1.225?

#9
Answer is D: 3 sqrt2

#10
Answer is D: 84

---

"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Special Right Triangles

I've just logged on.  I'll check them now.

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Special Right Triangles

All correct.  Well done!

Do you need hints for 11-20 or are you ok with these now?

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

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Special Right Triangles

Yes I think that would be great if you could help out a little with those.

---

"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Special Right Triangles

OK

If you have a 30-60-90 triangle:

11. And the length of the shortest leg is 4, what's the length of the hypotenuse? - Answer: 8   correct
A 5
B12
C20
D52
E 8
F 4

12. Working from #11, what's the length of the other leg? - Answer: 6 (i understand that is is 4(square root 3), 4 x 4 = 16, 16 x 3 = 48 then square root this to get the answer. is my method correct?)

  Yes but the answer isn't 6 but rather 6 and a bit

leg = sqrt(8^2 - 4^2) = sqrt 48

A 3.0713
B4.1579
C9.2357
D6.9282
E 10.084
F 9.1157

13. And the length of the longest leg is 5[SQRT(3)], what's the length of the other leg? - Answer: E   correct
A 2
B7
C16
D27
E 5
F 24

14. Working from #13, what's the length of the hypotenuse? - Answer: A correct 
A 10
B24
C57
D91
E 39
F 46

15. And the length of the longest leg is 9, what is the length of shortest leg?

Note:  in this triangle the sides are in the ratio 2 : √3 : 1 

so you need to divide by root 3

A 6sqrt5
B9sqrt2
C5sqrt6
D7sqrt5
E 4sqrt2
F 3sqrt3

16. Working from #15, what is the length of the hypotenuse?

and then double that answer 

A 2sqrt5
B3sqrt4
C8sqrt9
D6sqrt3
E 10sqrt2
F 7sqrt4

17. With a hypotenuse of 2[SQRT(3)] what is the length of the longest leg?

Use this ratio 2 : √3 : 1  here too

A 7
B33
C9
D27
E 3
F 14

18. Working from #17, what is the length of the shortest leg?

and  here

A 1.7321
B1.9443
C1.8459
D1.2946
E 1.0906
F 1.6504

19. And the length of the shortest leg is SQRT(12), what is the length of the longest leg?

and  here

A 29
B6
C38
D56
E 61
F 17

20. Working from #19, what is the length of the hypotenuse?

and  here

A 8.4197
B1.9764
C10.5742
D6.2414
E 2.4971
F 6.9282

Hope that helps.

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

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Special Right Triangles

#15.
9 divided by 3 = 3
and
3 x 3 = 9
So I will choose F: 3 sqrt3

#16.
I choose D: 6 sqrt3

#17.
I choose E: 3

#18.
I choose A: 1.7321

#19.
not too sure how to solve it with just a SQRT(12)

---

"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Special Right Triangles

Q15 to Q18 all correct, well done!

Q19:  work from the ratio 2 : √3 : 1

If the shortest leg is root 12 that means you have to scale up the ratios by this factor

2 x root 12 : root3 x root 12 : 1 x root 12

So now you have to simplify root 3 x root 12 (it comes out to a simple number)

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

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Special Right Triangles

So that means (sqrt3) x (sqrt12) = (sqrt36)
Square that and I get 6 which is answer B: 6

#19.
Answer is B: 6

#20.
Answer is D: 6.2414

---

"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Special Right Triangles

Q19  That's my answer.

Q20  But not this one ??

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