Question

Part A. In triangle ABC angle A is a right angle and m angle B =45 degrees.

Part B. what is the length of BC? If your answer is not an integer, leave it in simplest radical form.

Answer 1

Since angle A is a right angle, we can label it as 90 degrees.

Since angle B is 45 degrees and angle A is a right angle, we can conclude that angle C is also 45 degrees. This is because the sum of angles in a triangle is always 180 degrees. Therefore, 90 + 45 + 45 = 180 degrees.

In triangle ABC, angles B and C are equal, meaning that sides BC and AC are also equal. Let's label the length of BC as x.

Using the properties of a right triangle with a 45-degree angle, we know that the sides opposite the 45-degree angles are equal. Therefore, side AB is also equal to x.

Now, let's use the Pythagorean theorem to find the length of side BC.

Using the theorem, we have:

AC^2 = AB^2 + BC^2

Substituting the values we have:

x^2 = x^2 + BC^2

Simplifying:

x^2 - x^2 = BC^2

0 = BC^2

Therefore, BC = 0.

In the given information, there seems to be some contradiction or mistake, as it is not possible for side BC to have a length of zero.