in triangle abc the radian measure of angle c is pi/6, what is the length of bc? ab = 2
i was thinking of taking the sin of pi/6 since bc is the y axis. but it does not match the answer of 2 root 3
To find the length of side BC in triangle ABC, we can use the Law of Sines. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. In other words:
BC / sin(angle C) = AB / sin(angle A) = AC / sin(angle B)
In this case, we are given that AB = 2 and angle C = π/6. We need to find BC.
Let's first find angle A. Since the sum of the angles in a triangle is always π radians (180 degrees), we can use the fact that angle A + angle B + angle C = π to solve for angle A:
angle A + π/6 + π/2 = π
angle A = π - π/6 - π/2
angle A = 2π/3
Now, we can plug in the values into the Law of Sines equation:
BC / sin(π/6) = 2 / sin(2π/3)
To simplify this equation, we need to determine the sine values of π/6 and 2π/3.
sin(π/6) = 1/2
sin(2π/3) = √3/2
Now, we can rewrite the equation:
BC / (1/2) = 2 / (√3/2)
To solve for BC, we can cross-multiply:
BC = (2 * 1) / (√3/2)
BC = 2 * 2/√3
BC = 4/√3
To rationalize the denominator, we can multiply both the numerator and the denominator by √3:
BC = (4 * √3) / (√3 * √3)
BC = (4√3) / 3
So, the length of BC is (4√3) / 3, which is approximately equal to 2.31.