Question

Explain why angle d must be a right angle

Pls help​

Answer 1

see explanation

Explanation:

Using Pythagoras' identity

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

Consider the right triangle on the right and calculate n

n² + 2² = 3²

n² + 4 = 9 ( subtract 4 from both sides )

n² = 5 ( take the square root of both sides )

n =
`√(5)`

If the triangle on the left is right then the square of the longest side must equal the sum of the squares on the other 2 sides.

The longest side is n =
`√(5)` ⇒ n² = (
`√(5)` )² = 5 and

(
`√(2)` )² + (
`√(3)` )² = 2 + 3 = 5

Hence D is a right angle