How to find the length of the side leg of the right triangle?

Question

My question states:

"Find the length of the side leg of the right triangle given the lengths of the base and the hypotenuse"

1)a=5,c=9

2)a=√2,c=√7

Answer 1

1. b = 3 - √5
2. b = √5

Answer 2

Use the Pythagorean theorem, c^2 = a^2 + b^2

c stands for the hypotenuse, and a and b the sides.

In 1, we would have

9^2 = 5^2 + s^2
81 = 25 + s^2
56 = s^2
s = sqrt(56) = 2sqrt(14)

Ignore Keith's answer for 1). He is wrong. No triangle can be formed from 9, 5, and such a short side as he proposes, shorter than 1. It wouldn't reach.

Both Keith and Ilurb have trouble knowing what and when to square. Be careful.

In 2)

7 = 2 + s^2
5 = s^2
s = sqrt(5)

Puzzling and Openpsychy agree with both my answers, and I agree with theirs.

Auequine doesn't know how to spell Pythagorean.

It's the scarecrow, not the lion, who recites the theorem when he gets his brain. The lion gets courage.

And bullet head makes no sense at all. No wonder the Germans lost World War II.

Answer 3

Hi. In the first problem set up as the previous answerer's suggested. Find the square of the hypotenuse. Subtract the square of the known side. Take the square root of the remainder.

Same with the second problem. And ALL problems of this nature.

Answer 4

Pthegorean Thorem

c² = a² + b²

c² - a² = a² + b² - a²

c² - a² = b² . . . .use this formula

- - - - - - - - - - - - -

c² - a² = b²

√(9)² - (5)² = b²

√81 - 25 = b²

√56 = b²

√4 √14 = b²

2 √14 = b

- - - - - - -s-

Answer 5

lets call the three sides of the triangle a b and c
c being the hypo. the sum of a plus b squared
is equal to the square of c 3(a) plus 4(b) squared equals 49 49 is the square of c which
is 7

Answer 6

h^2 = a^2 + b^2
Just remember what the Lion said in the Wizard of Oz,
"The sum of the squares of the two legs of any right triangle is equal to the square of the hypotenuse (longest side)."

Answer 7

Use Pythagorean theorem solving for that side.

Write it as b squared = c squared - a squared.

1)
Plug in the value of a and c so you get 9x9 - 5x5 which = 81-25
That equals 56 = b squared. Taking the square root you get a = 7.48
2)
Plug in the value of a and c so you get square root of 7 x square root of 7- square root of 2 x square root of 1 which = 7-2
That equals 5 = b squared. Taking the square root you get a = 2.24

Answer 8

Pythagorian theorum! You can learn it simply by watching the Wizard or Oz, it's what the scarcrow recites when he gets his brain!
a^2+b^2=c^2
5^2+b^2=9^2
25+b^2=81
b^2=56
b=square root 56

Answer 9

Pythagorean theorem:
a² + b² = c²

Solving for b:
b = sqrt(c² - a²)

So plug in your values:
1) a = 5, c = 9
b = sqrt(9² - 5²)
b = sqrt(81 - 25)
b = sqrt(56)
b = 2 sqrt(14)

2) a = sqrt(2), c = sqrt(7)
b = sqrt(sqrt(7)² - sqrt(2)²)
b = sqrt(7 - 2)
b = sqrt(5)

Answer 10

use a^2+b^2=c2
now find b so its
b^2 = c^2-a^2
plug everything in