Question

(Please help!) Use the converse of the Pythagorean theorem to decide if the triangles are right, acute or obtuse. Then classify them

label where a, b, c is

thanks so much

Answer 1

• 
  `\sf Right \: triangle`

Explanation:

Pythagoras theorem states that, The square of the longest side of the triangle is equal to the sum of the other two sides of the triangle.

i.e a² + b² = c² [where c is the longest side of the triangle and a and b are the other two sides]

If a² + b² < c² then the triangle is obtuse.

If a² + b² > c² , then the triangle is acute.

If a² + b² = c² , then the triangle is right angled.

Let's solve,

From the given diagram, Longest side (c) is 41 and the other two sides (a and b) are 9 and 40 .

Using Pythagoras theorem,

»
`\sf a^2 + b^2 = c^2`

»
`\sf9^2 + 40^2 = 41^2`

»
`\sf 81 + 1600 = 1681`

»
`\sf 1681 = 1681`

Since, a² + b² = c². Therefore The given triangle is right angled.