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**demha****Member**- Registered: 2012-11-25
- Posts: 195

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,009

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

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**demha****Member**- Registered: 2012-11-25
- Posts: 195

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,009

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

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**demha****Member**- Registered: 2012-11-25
- Posts: 195

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

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**demha****Member**- Registered: 2012-11-25
- Posts: 195

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,009

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

Bob

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,009

All correct. Well done!

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

Bob

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**demha****Member**- Registered: 2012-11-25
- Posts: 195

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,009

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

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**demha****Member**- Registered: 2012-11-25
- Posts: 195

#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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,009

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

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**demha****Member**- Registered: 2012-11-25
- Posts: 195

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,009

Q19 That's my answer.

Q20 But not this one ??

Bob

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