Questions: In the picture above CB=18 and AC=14. Solve for AB. Round your answer to the tenths place if necessary.

Transcript text: In the picture above $C B=18$ and $A C=14$. Solve for $A B$. Round your answer to the tenths.place if necess

Solution

Solution Steps

Step 1: Identify the type of triangle

Triangle ABC is a right triangle, with angle B being the right angle.

Step 2: Apply the Pythagorean theorem

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, AC is the hypotenuse, and CB and AB are the other two sides. So we have:

AC² = AB² + CB²

Step 3: Substitute the given values and solve for AB

Substituting the given values, we get:

14² = AB² + 18²

196 = AB² + 324

AB² = 196 - 324

AB² = -128

Since the square of a length cannot be negative, there must be an error in the given information. The lengths of the sides of a right triangle must satisfy the Pythagorean theorem. It's possible the labels of AC and CB are switched. Let's try that.

Step 4: Apply Pythagorean theorem with switched sides

Assuming CB is the hypotenuse: 18² = AB² + 14² 324 = AB² + 196 AB² = 324 - 196 AB² = 128 AB = √128 AB ≈ 11.3