Math Is Fun Forum

demha

Member

Registered: 2012-11-25

Posts: 195

Review

This is a review I need to do. It will involve Triangles, Sohcahtoa, Pythagorean Theorem and the Special Right Triangles (30 - 60 - 90 and 45 - 45 - 90). Please help me understand them and check if they are correct: (NOTE FOR #3 and #4, there must be something wrong. I thing I am doing something wrong in #3. Help would be appreciated! I would like to learn a method to find the answer if mine is wrong.)
1.

Q. A 30-60-90 triangle has a hypotenuse of 10. Use trig to find the short side. Show your work.

A. Answer is 5. Shortest side is always half of the hypotenuse. The longest side would be the shortest leg and (sqrt3).

2.

Q. A 30-60-90 triangle has a hypotenuse of 10. Use special right triangle formulas to find the long side. Show your work.

A. We understand that the shortest leg is 5.
The shortest leg is 5.
The hypotenuse is (5 x 2) or 10.
The longest leg will be 5 (sqrt3)
The final answer for the longest leg will be 8.660

3.
Q. A 30-60-90 triangle has a hypotenuse of 16 and a short side of 8. Use the Pythagorean theorem to find the third side. Show your work.

A.
a^2 + b^2 = c^2
8^2 + 16^2 = c^2
64 + 256 = c^2
320 = c^2
(after squaring)
C = 17.888

4.
Q. A 30-60-90 triangle has a hypotenuse of 16 and a short side of 8. Use special right angle formulas to find the third side. Show your work. Does your answer match what you got on number 3?

A.
8 (sqrt3) = 13.856

5.
Q. A 45-45-90 triangle has a leg of 4[sqrt(2)]. What is the hypotenuse? Show your work.

A.
4 (sqrt2) x (sqrt2) = 4 (sqrt4) = 8

6.
Q. A right triangle has legs of 4 and 5. What is the hypotenuse? Show your work.

A.
a^2 + b^2 = c^2
4^2 + 5^2 = c^2
16 + 25 = c^2
41 = c^2
(after squaring)
C = 6.403

7.
Q. A right triangle has a hypotneuse of 13 and a leg of 8. What is the other leg? Show your work.

A.
13^2 - 8^2 = b^2
13^2 - 8^2 = b^2
169 – 64 = b^2
105 = b^2
(after squaring)
B = 10.246

8.
Q. A 12-foot ladder is leaning across a fence and is touching a higher wall located 3 feet behind the fence. The ladder makes an angle of 60 degrees with the ground. Find the distance from the base of the ladder to the bottom of the fence.

A.
NOTE: not sure exactly how to do this, I would appreciate a method on how to solve this one too.

cheers

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"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: Review

1.

Q. A 30-60-90 triangle has a hypotenuse of 10. Use trig to find the short side. Show your work.

A. Answer is 5. Shortest side is always half of the hypotenuse. The longest side would be the shortest leg and (sqrt3).

correct. 

2.

Q. A 30-60-90 triangle has a hypotenuse of 10. Use special right triangle formulas to find the long side. Show your work.

A. We understand that the shortest leg is 5.
The shortest leg is 5.
The hypotenuse is (5 x 2) or 10.
The longest leg will be 5 (sqrt3)
The final answer for the longest leg will be 8.660

correct. 
3.
Q. A 30-60-90 triangle has a hypotenuse of 16 and a short side of 8. Use the Pythagorean theorem to find the third side. Show your work.

A.
a^2 + b^2 = c^2
8^2 + 16^2 = c^2
64 + 256 = c^2
320 = c^2
(after squaring)
C = 17.888

   Too big.  You've muddled up which side is which in the formula.
4.
Q. A 30-60-90 triangle has a hypotenuse of 16 and a short side of 8. Use special right angle formulas to find the third side. Show your work. Does your answer match what you got on number 3?

A.
8 (sqrt3) = 13.856

Correct. 
5.
Q. A 45-45-90 triangle has a leg of 4[sqrt(2)]. What is the hypotenuse? Show your work.

A.
4 (sqrt2) x (sqrt2) = 4 (sqrt4) = 8

Correct.   
6.
Q. A right triangle has legs of 4 and 5. What is the hypotenuse? Show your work.

A.
a^2 + b^2 = c^2
4^2 + 5^2 = c^2
16 + 25 = c^2
41 = c^2
(after squaring)
C = 6.403

  correct.
7.
Q. A right triangle has a hypotneuse of 13 and a leg of 8. What is the other leg? Show your work.

A.
13^2 - 8^2 = b^2
13^2 - 8^2 = b^2
169 – 64 = b^2
105 = b^2
(after squaring)
B = 10.246

  correct.
8.
Q. A 12-foot ladder is leaning across a fence and is touching a higher wall located 3 feet behind the fence. The ladder makes an angle of 60 degrees with the ground. Find the distance from the base of the ladder to the bottom of the fence.

A.
NOTE: not sure exactly how to do this, I would appreciate a method on how to solve this one too.
  Have you made a diagram?  Using 12 and the special formula you can work out base of ladder to wall.  Then it's easy.

Bob

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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: Review

#3.
b = c^2 - a^2?
b = 16^2 - 8^2
b = 256 - 64
b = 192
(after squaring)
13.856 = b

I DID IT!!

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#8.
I uploaded an image of my diagram. Not too sure if its correct though. And what kind of equation would I be making?

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

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Review

image

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"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: Review

Hi demha

Well done for sorting out Q3.

For Q8, I think the questioner intends that the ladder just scrapes the top of the fence. (Actually now I think about it, there is no need to assume this.  You can do the question anyway.)  I have copied your diagram but made the fence taller and labelled the points.

You know CAB = 60 and AC = 12, so you can work out AB

You also know DB = 3.

So you can work out AD.

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: Review

So do I do this:
cos(60) = g/12
.5 = g/12
g = 12 x .5
g = 6

So the ladder is 6 feet away from the wall, then we do:
6 - 3 = 3.
The base of the ladder from the bottom of the fence is 3 ft.

Is this method correct?

Last edited by demha (2013-08-12 14:09:58)

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"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: Review

Yes, that will do nicely. 

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: Review

Hi Bob,
My teacher said everything is correct, but for number 1 she wants me to use trigonometry to solve it. Here is the question again with my original answer:
1.

Q. A 30-60-90 triangle has a hypotenuse of 10. Use trig to find the short side. Show your work.

A. Answer is 5. Shortest side is always half of the hypotenuse. The longest side would be the shortest leg and (sqrt3).

---

What equation (or method) am I supposed to use exactly?

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

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Review

Would this method be correct?
cos(30)=x/10
10 cos(30) = x
cos(30) = 1/2
so10 *1/2 = 5

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"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: Review

The smallest side is opposite the smallest angle.  Using SOH CAH TOA you know H and the angle (30) and want 'O'

So

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