So

Bob

]]>cos(30)=x/10

10 cos(30) = x

cos(30) = 1/2

so10 *1/2 = 5]]>

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?

]]>Bob

]]>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?

]]>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

]]>b = c^2 - a^2?

b = 16^2 - 8^2

b = 256 - 64

b = 192

(after squaring)

13.856 = b

I DID IT!!

---

#8.

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

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

]]>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

]]>