The measures of the sides of a triangle are 19, 15, and 13. Use the Pythagorean Theorem to classify the triangle as acute, obtuse, or right

Question

The measures of the sides of a triangle are 19, 15, and 13. Use the Pythagorean Theorem to classify the triangle as acute, obtuse, or right.

Answer 1

It is not a right triangles because 15^2 + 13^2 is NOT EQUAL to 19^2

let x, y, and z be the angles inside the triangle.

Law of cosines says:

19^2 = 13^2 + 15^2 - 2(13)(15)cos x

361 = 169 + 225 - 390 cos x

-33 = -390 cos x

-33/-390 = cos x

11/130 = cos x

x = inverse cosine (11/130)

= 85.14609471338569.....

Per law of sines:

sin x/19 = sin y / 13

(13/19)sinx = sin y

inverse_sine ( (13/19) sin x) = y

y = 42.9810733896016548....

Per law of sines

sin x/19 = sin z / 15

z = inverse_sine( (15/19) sin x)

= 51.8728352950227805....

So it is an acute triangle and yes, these angles add up to 180