Question

The triangle ABC angle a is a right angle and angle and M angle b equals 45 degrees what is the length of BC if your answer is not an integer leave it in the simplest radical form

Answer 1

Given that angle A is a right angle (90 degrees) and angle B is 45 degrees, we can use the trigonometric ratios to find the length of BC.

Let x be the length of BC.

Using the sine function:
sin(45 degrees) = BC/AC
sin(45) = x/AC
1/sqrt(2) = x/AC
AC = x / (1/sqrt(2))
AC = x * sqrt(2)

Using the Pythagorean theorem in triangle ABC:
(AC)^2 = (AB)^2 + (BC)^2
(AC)^2 = (x)^2 + (x*sqrt(2))^2
(AC)^2 = x^2 + 2x^2
(AC)^2 = 3x^2

Substitute AC = x * sqrt(2):
(x * sqrt(2))^2 = 3x^2
2x^2 = 3x^2
2 = 3

This equation shows that there is no solution for x that satisfies the given conditions. Therefore, the length of BC cannot be determined.