Question

The lengths of the sides of a triangle are 6, 7 and 9. Classify the triangle as acute, right or obtuse.

Answer 1

To determine if the triangle is acute, right, or obtuse, we need to find the largest angle of the triangle. We can do this by using the Law of Cosines.

Let a, b, and c be the sides of the triangle with lengths 6, 7, and 9 respectively.

Let A, B, and C be the angles of the triangle opposite to sides a, b, and c respectively.

Using the Law of Cosines, we have:
c^2 = a^2 + b^2 - 2ab * cos(C)

Substitute the given values:
9^2 = 6^2 + 7^2 - 2*6*7*cos(C)
81 = 36 + 49 - 84cos(C)
81 = 85 - 84cos(C)
84cos(C) = 4
cos(C) = 4/84
cos(C) = 1/21
C = cos^(-1)(1/21)
C ≈ 83.64 degrees

Since angle C is approximately 83.64 degrees, the triangle is acute.