Question

The side lengths of triangle ABC are expressed in terms of the variable p, where p=23. Which statement is correct regarding the angles of the triangle?

A. ∠A>∠C>∠B
B. ∠B>∠∠A>∠C
C. ∠C>∠B>∠A
D. ∠C>∠A>∠B

Answer 1

Based on the given side lengths of triangle ABC, the correct statement regarding the angles is ∠A > ∠C > ∠B.

Step-by-step explanation:

In a triangle, the sum of the three angles is always 180 degrees. So, to determine the relationship between the angles of triangle ABC, we need to consider the side lengths. Since the side lengths are expressed in terms of the variable p, we can substitute p=23 into the equation to find the relationship. Let's denote the side lengths as a, b, and c, where a is opposite to angle A, b is opposite to angle B, and c is opposite to angle C. Based on the given information, we have:

1. Side length a = 23p
2. Side length b = 23
3. Side length c = 23p

To determine the relationship between the angles, we need to compare the side lengths. Since side length b is constant (23), it does not affect the angle measurements. Thus, we can compare side lengths a and c. Since a and c both have the variable p, we can compare the coefficients in front of p to determine the relationship:

1. If the coefficient in front of p for side length a is greater than the coefficient in front of p for side length c, then angle A is greater than angle C.
2. If the coefficient in front of p for side length a is less than the coefficient in front of p for side length c, then angle A is less than angle C.
3. If the coefficients in front of p for side lengths a and c are equal, then angle A is equal to angle C.