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

• Acute triangle

Step-by-step 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 8 and the other two sides (a and b) are 4 and 7 .

Using Pythagoras theorem,

»
`\sf a^2 + b^2 = c^2`

»
`\sf4^2 + 7^2 = 8^2`

»
`\sf 16 + 49 = 64`

»
`\sf 65 > 64`

Since, a² + b² > c². Therefore The given triangle is acute.

Answer 2

acute triangle

Explanation:

a = 4 , b = 7 , c = 8

• if a² + b² = c² , then triangle is right

• if a² + b² > c² , then triangle is acute

• if a² + b² < c² , then triangle is obtuse

c² = 8² = 64

a² + b² = 4² + 7² = 16 + 49 = 65

since a² + b² > c² , then the triangle is acute