What is the sine of a 30 degree angle? I need help. I don't know how to do this. The answer choices I have must be the square root of the sine 30 degrees.
Thanks!
Jason Crocker
Hi Jason! I believe it is Square Root 3. I assume you're in K12? Me too!
You must have the answers provided here, Jason, for us to answer.
Time to review the special angles:
sin(30°) = 1/2
so,
√sin(30°) = 1/√2
also,
cos(30°) = √3/2
To find the sine of a 30 degree angle, you can use a trigonometric table, a scientific calculator, or a trigonometric function. In this case, since you already have the answer choices in the form of the square root of the sine of 30 degrees, we can use the trigonometric function directly.
To calculate the sine of 30 degrees, you can use the sine function, denoted as sin(x), where x represents the angle in radians or degrees.
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
For a 30 degree angle, you can create a right triangle with one of the acute angles measuring 30 degrees. Let's label the sides of the triangle:
- The side opposite the 30 degree angle is usually denoted as the length "a".
- The hypotenuse (the longest side) is usually denoted as "c".
In a 30-60-90 degree triangle, the ratio of the side opposite the 30 degree angle to the hypotenuse is always 1:2. Therefore, a/c = 1/2.
Using the Pythagorean theorem, we can find the value of the missing side, which is the length "a". The Pythagorean theorem states that in a right triangle, the sum of the squares of the two legs (the shorter sides) is equal to the square of the hypotenuse:
a^2 + (2a)^2 = c^2
a^2 + 4a^2 = c^2
5a^2 = c^2
Given that the ratio of a/c is 1/2, we know that c is twice the value of a. Therefore, we can substitute 2a for c in the equation:
5a^2 = (2a)^2
5a^2 = 4a^2
5a^2 - 4a^2 = 0
a^2 = 0
Solving for "a", we find that "a" is 0.
Now that we have the side lengths of the triangle, we can find the sine of 30 degrees:
sin(30 degrees) = a/c = 0/2 = 0
Therefore, the sine of a 30 degree angle is 0.