Question

Use the converse of the Pythagorean theorem to decide if the triangle is right, acute or obtuse. Then classify them

please help, thanks so much!!!

Answer 1

A = 6
B = 7
C = Hypotenuse = longest side = 9

Right triangle:
C squared = A squared + B squared

Obtuse:
C squared > A squared + B squared

Acute:
C squared < A squared + B squared

A squared=6 squared = 6x6= 36
B squared=7squared = 7x7= 49
C squared=9 squared = 9x9= 81

A squared + B squared is:

36+49
So it is 85

C squared is 81 so it is less than 85.

Since C squared < A squared+B squared,

This is an acute triangle.

Answer 2

acute triangle

Explanation:

using the converse of the Pythagorean theorem.

if the square on the longest side is equal to the sum of the squares on the other two sides then the triangle is right.

let c be the longest side and a, b the two legs , then

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

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

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

here c = 9 , a = 6 , b = 7

c² = 9² = 81

a² + b² = 6² + 7² = 36 + 49 = 85

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