In triangle ABC, mc002-1.jpg is a right angle and mc002-2.jpg 45°

Question

;. Find BC. If your answer is not an integer, leave it in simplest radical form.

Answer 1

Based on the given information, we have a right triangle ABC with angle C being 90 degrees and angle B being 45 degrees.

We know that the angles in a triangle add up to 180 degrees, so angle A is 180 - 90 - 45 = 45 degrees.

Since angle B and angle A are both 45 degrees, triangle ABC is an isosceles right triangle.

In an isosceles right triangle, the lengths of the two legs (AB and BC) are equal.

Let's assume the length of AB and BC is x.

Using the Pythagorean theorem, in a right triangle, the square of the hypotenuse (AC) is equal to the sum of the squares of the two legs.

AC^2 = AB^2 + BC^2
BC^2 = AC^2 - AB^2
= (x^2) - (x^2)
= 0

This means that if the length of AB is x, the length of BC is also x, which makes BC = x.

Therefore, the length of BC is equal to the length of AB, and since it is not given, we cannot determine the exact value of BC. We can only say that BC is also x, and this value is not an integer.