Question

I need help understanding which is a,b, or c​

Answer 1

a) the hypotenuse is known but we aren't finding the hypotenuse
Using Pythagoras' Theorem
side²= hyp² -side²

side²= 74²-24²

= 4900

side²=√4900

70

Therefore the unknown side is 70

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b) Now in this problem, we have to find the hypotenuse
Using Pythagoras' Theorem
hyp²= side²+side²

hyp²= 40²+40²

= 3200

=56.56

Therefore the hypotenuse is 56.56

NB: IF YOU HAVE TO FIND THE HYPOTENUSE, YOUR ANSWER IS WRONG IF THE HYPOTENUSE IS SMALLER THAN THE GIVEN VALUES BECAUSE, AS YOU KNOW, THE HYPOTENUSE IS THE LONGEST SIDE IN A RIGHT-ANGLED TRIANGLE.

HOPE THIS HELPS! ;-)

Answer 2

see explanation

Explanation:

Using Pythagoras' theorem, that is

The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.

Using x instead of ?

(a)

The hypotenuse is the side opposite the right angle, that is 74, thus

24² + x² = 74²

576 + x² = 5476 ( subtract 576 from both sides )

x² = 4900 ( take the square root of both sides )

`\sqrt{x^(2) }` =
`√(4900)`

x = 70

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(b)

The hypotenuse x is the unknown side here

x² = 40² + 40² = 1600 + 1600 = 3200

Take the square root of both sides

`\sqrt{x^(2) }` =
`√(3200)` ≈ 56.6 ( nearest tenth )