pythagoren theorem problems!!!!?

Question

1) a=? b=8 c=17

2) a=3 b=? c=5

3) a=9 b=? c=15

please help!!!!
and show the work

thxs sooo much

Answer 1

(1)
a² + b² = c² [Substitute values for b and c.]
a² + (8)² = 17² [Evaluate the squares.]
a² + 64 = 289 [Subtract 64 from each side.]
a² = 225 [Take the square root of each side.]
√(a²) = √225 [Evaluate the square roots.]
| a | = 15 [Solve for a.]
a = ±15 [Since a is a length, the negative root is ignored.]
a = 15

(2)
a² + b² = c² [Substitute values for a and c.]
(3)² + b² = 5² [Evaluate the squares.]
9 + b² = 25 [Subtract 9 from each side.]
b² = 16 [Take the square root of each side.]
√(b²) = √16 [Evaluate the square roots.]
| b | = 4 [Solve for b.]
b = ±4 [Since b is a length, the negative root is ignored.]
b = 4

(3)
a² + b² = c² [Substitute values for a and c.]
(9)² + b² = 15² [Evaluate the squares.]
81 + b² = 225 [Subtract 81 from each side.]
b² = 144 [Take the square root of each side.]
√(b²) = √144 [Evaluate the square roots.]
| b | = 12 [Solve for b.]
b = ±12 [Since b is a length, the negative root is ignored.]
b = 12

Answer 2

c^2 = a^2 + b^2 (think of in terms of a triangle, c being the longest side and a and b are the shorter two that must add up to the c)
Simple substitution is all that is left:
1. 17^2 = a^2 + 8^2
289 = a^2 + 64
289-64=a^2
225 = a^2 (at this point I like to put "a" term on left side so:
a^2 = 225
At this point "a^2" needs to be a single "a." To rid ourselves of the squared a we simply take the square root of 225. REMEMBER in doing so that it results in + and - the square root. If you are dealing with trig. most the time you ignore the negative value, or what your question is asking for make sure that it would make sense to reply with a negative number or if the question is only looking for the positive portion of the square root.
a = +15 and -15

2. 5^2 = 3^2 + b^2
25 = 9 + b^2
16 = b^2 ( I like to switch here)
b^2 = 16
b = +4 and -4

3. 15^2 = 9^2 + b^2
225 = 81 + b^2
144 = b^2 (Switch)
b^2 = 144
b = +12 and -12

Answer 3

Hi. Do not get hung up on the complicated name. The concept is simple. In right triangles (this just means they have a square corner) there is a simple relationship to all three sides. The two sides that connect the square corner are called "adjacent" (to the corner), or in some problems "opposite" (from an angle). The side at an angle and opposite to the square corner is called the "hypotenuse". Again don't get hung up on the name for now.

Here is the deal and if you understand this trig will be a MUCH easier subject for you. If you make a square from each side of the triangle then the AREA OF THE SQUARE of one adjacent side (near the corner) and the AREA OF THE SQUARE of other adjacent side added together equals the AREA OF THE SQUARE OF THE HYPOTENUSE.

The easiest triangle to see this on is called a 3,4,5. The sides equal 3 units, 4 units, and 5 units. Units can be anything but let's call them feet for now. 3 and 4 are the adjacent sides. 3 squared (3x3) equals 9, and 4 squared (4x4) equals 16. 16 + 9 equals 25. 5 squared (5x5) equals 25. So, if you know ANY TWO SIDES you can find the length of the third.

If you can learn the above you will get to love trig. I mean it.

Now plug the values into your formula. I know lots of people have done this for you but do it anyway until you understand. Love to learn. It will make your world happier!

Answer 4

I'm not doing your homework for you. But not to rule out the possibility that you're having genuine problems with the Pythagorean theorem, I'll show you the second problem- one that you should know by heart because 3-4-5 is the most basic of the Pythagorean triples.

2) a^2 + b^2 = c^2
b = sqrt[ c^2 - a^2 ] = sqrt [ 5^2 - 3^2 ] = sqrt [ 16 ] = 4

Answer 5

The formula you need to use is a^2 + b^2 = c^2.

So for question 1:

a^2 + 8^2 = 17^2
a^2 = 289 - 64
a = sqrt. 225 = 15

Therefore a = 15.

You can work out the rest in a similar way.

Answer 6

1) a=? b=8 c=17

x squared + 64= 289
subtract 64 from both sides
x squared= 225
then find the square root of 225 on a calculator

2) a=3 b=? c=5

9 + x squared= 25
subtract 9 from both sides
x squared= 16
find the square root of 16

3) a=9 b=? c=15

81 + x squared= 225
subtract 81 from both sides
x squared= 144
find the square root of 144

Answer 7

a^2+b^2=c^2 is the pythagorean theorem.

1) a^2+8^2=17^2 a^2+64=289 289-64=a^2 a=15

Answer 8

a^2 + b^2 = c^2
just plug in the numbers. solve for the missing variable.

Answer 9

R-Diz is right. Just use the formula and plug in the numbers. You can do it.