In triangle ABC the measure of <A is a right angle and the measure of <B = 45 degrees. What is the length of BC? (1 point) Responses 182–√ 18 square root of 2 183–√ 18 square root of 3 36 36 18
The triangle is a right triangle, with angle B equal to 45 degrees. This means that angle C is 45 degrees as well, as the sum of the interior angles of a triangle is always 180 degrees.
Since angle C is 45 degrees, triangle ABC is a 45-45-90 triangle. In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is equal to the square root of 2 times the length of one of the legs.
Let's call the length of BC x. Since BC is one of the legs of the triangle, AC (the other leg) is also x. The hypotenuse, AB, is x * √2.
We know that BC = x, so in this case, BC = x.
Therefore, the length of BC is square root of 2 times x, which simplifies to x√2. Therefore, the length of BC is 36√2.
So, the correct option is the square root of 2.