3.) 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 183–√ 18 square root of 3 36 36 182–√ 18 square root of 2 18
The measure of angle C in a right triangle can be found using the property that the sum of the angles in a triangle is 180 degrees. Since angles A and B are already given, we can find angle C:
180 = 90 + 45 + C
180 = 135 + C
C = 45 degrees
Now that we have all the angles of the triangle, we can use trigonometry to find the length of BC. Since angle B is 45 degrees, and the triangle is also a right triangle, we can use the properties of a 45-45-90 triangle.
In a 45-45-90 triangle, the legs are equal in length, and the length of the hypotenuse is √2 times the length of the legs.
Since the length of BC is the same as the length of AC in this triangle, BC = AC.
Let AC = x
BC = x
AC = x
Using the Pythagorean theorem:
x² + x² = (x√2)²
2x² = 2x²
x = x
Therefore, the length of BC is x, which is equivalent to AC.
So the answer is "square root of 2"