Question

If the length of one leg of a right triangle is 4 and the hypotenuse is √65 , what is the length of the other leg?

Answer 1

To answer this question you must use Pythagorean theorem

`a^(2) +b^(2)=c^(2)`

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 4

b = unknown

c =
`√(65)`

^^^Plug these numbers into the theorem

`4^(2) +b^(2) = √65^(2)`

Simplify

16 + b² = 65

solve for b

`b^(2)` + 16 = 65

`b^(2)` = 49

To completely isolate b you will have to get rid of the square attached to it. To do this you will need to take the square root of both sides

√b² = √49

b = 7

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer 2

7

Explanation:

Using Pythagoras' identity on the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the other leg, then

x² + 4² = (
`√(65)` )²

x² + 16 = 65 ( subtract 16 from both sides )

x² = 49 ( take the square root of both sides )

x =
`√(49)` = 7

That is the other leg is 7 units