Question

Classify a triangle with the following sides 23, 34 and 45
(1 point)
• Acute
• Obtuse
• Right

Answer 1

The triangle with sides 23, 34, and 45 is a scalene triangle. However, it is not a right triangle since the square of the longest side (45) is not equal to the sum of the squares of the other two sides (23^2 + 34^2 = 529 + 1156 = 1685).

Since it is not a right triangle, the only remaining possibilities are acute or obtuse. To determine whether it is acute or obtuse, we can use the law of cosines.

Let's label the sides of the triangle as follows:
a = 23
b = 34
c = 45

The law of cosines states:
c^2 = a^2 + b^2 - 2ab*cos(C)

Plugging in the values, we have:
45^2 = 23^2 + 34^2 - 2(23)(34)*cos(C)
2025 = 529 + 1156 - 1564*cos(C)
2025 = 1685 - 1564*cos(C)
340 = -1564*cos(C)

Since 340 is positive and -1564 is negative, the cosine of angle C must be negative. This means that angle C is obtuse. Therefore, the triangle with sides 23, 34, and 45 is an obtuse triangle.