math help plzzzzzz? 10 pts easliy?

Question

Okay so we're learning about the Pythagorean Theorem, and we're into Right Triangles (30,60,90's and 45,45) to be specific
1. One Leg of a 45 -45 right triangle is 15centimeters long. What is the length of the other leg?
2.The shorter leg of a 30 -60 right triangle is 3 inches long
a.What is the length of the hypotenuse?
b.What is the length of the other leg?
3.How do you find missing lengths in each right triangle?
4. The hypotenuse of a 45 -45 right triangle is 12cm long. Find the length of each of the other sides.
Thnx so much plz explain n give the answers if ya can im trying to see if my neice got them right, i worked them out n im not sure! plz help 10 pts to whoever can.

Answer 1

I hope you can learn from these answers, not just copy :-)
1 In 90 deg triangle, since angels are the same, legs are too, so the answer is 15 cm too
2 This is a known 3-4-5 triagle, so:
a.hypotenuse = 5
b.other leg = 4
3.Basically, if it's not a known triangle, then we have the sin function:
leg = hypotenuse * sin (angel opposite to leg)
(This can be reversed to calculate the hypotenuse too)
4. As mentioned above: since both have the same angel opposite to them both are the same length which is:
12 * sin (45) =~ 8.48

Answer 2

1. By pythagora's:
a^2 + b^2 = c^2
15^2 + 15^2 = c^2
c= sqrt(15^2 + 15^2)
c= 21.2cm (the side opposite the 90)
a = b = 15

2. Shortest leg would be the one opposite the angle of 30
Sine rule: sinA/a = sinB/ b = sinC / c,
where the uppercase are the angles, and the lowercase the sides opposite to the angles

a.therefore sin30/3 = sin90/hypotenuse
hypotenuse = 6 inches

b. sin30/3 = sin 60/other leg
other leg =5.19615242270663

3.By pythagora's theorm
a^2 + b^2 = c^2

4. 12^2 = a^2 + a^2 (since the triangle is a isosceles triangle)
144 = 2(a^2)
72 = a^2
a = 8.48528137423857

I don't agree with nbenuzi's solution for question 2

According to sine rule,

3/sin30 does not equal to 4/sin60 does not equal to 5/sin90

Answer 3

There are formulas for these, let me see if I can remember them.
good picture for the 45: http://www.krellinst.org/UCES/archive/resources/trig/p6-1.gif

a would be the hypotenuse.

The legs of a 45-45-90 are the same value.

Now for the 30-60-90 triangle:

http://www.eurekareview.com/images/questionMath4Y.gif

x would be the shortest leg