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