in RIGHT 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
I would have to know where the right angle is.
You are clearly dealing with the 30,60,90º triangle which has sides 1,√3,2 respectively.
π/6 radians = 30º, and you give me 2 unit as the side across from the 30º angle.
so 2√3 makes sense as the side across form 60º (2π/6)
To find the length of side BC in right triangle ABC, you can use the trigonometric ratios sine, cosine, or tangent. Since angle C is given as π/6 (which is equivalent to 30 degrees), and side AB is given as 2 units, you can use the sine ratio to find the length of side BC.
The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, BC is the side opposite angle C, and AB is the hypotenuse.
Let's use the sine ratio:
sin(π/6) = opposite/hypotenuse
sin(π/6) = BC/2
To find BC, rearrange the equation:
BC = 2 * sin(π/6)
Now, substitute the value of sin(π/6):
BC = 2 * (1/2)
BC = 1
The length of side BC is 1 unit, not 2√3 as you had expected. Please double-check your inputs and the given information to ensure accuracy.
To solve this problem, we can utilize the properties of a 30-60-90 right triangle. In this triangle, the sides have a ratio of 1:√3:2.
Given that angle C has a radian measure of π/6, which is equivalent to 30 degrees, we can deduce that side BC is opposite the 60-degree angle.
Since side AB is given as 2 units, we are trying to find the length of side BC. In a 30-60-90 triangle, the side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.
Therefore, BC = AB * √3 = 2 * √3 = 2√3 units.
Hence, the length of BC is 2√3 units.