What is the value of x if it’s a 38 degree triangle and two sides of 21
x=71
To find the value of x in a triangle, given that it is a 38 degree triangle with two sides of 21, we can use the law of sines.
The law of sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Mathematically, this can be represented as:
a / sin(A) = b / sin(B) = c / sin(C),
where a, b, and c are the lengths of the sides, and A, B, and C are the opposite angles.
In this case, we know that one angle is 38 degrees, and the corresponding side is 21. Let's call this angle A and the side opposite it a. We are trying to find the length of side b (x in this case), which is opposite to angle B.
Using the law of sines, we can set up the following equation:
21 / sin(38) = x / sin(B).
Now, we can solve for x by rearranging the equation:
x = (21 * sin(B)) / sin(38).
To find sin(B), we need to remember that the sum of angles in any triangle is always 180 degrees. Therefore, angle C (opposite side c) can be found by subtracting 38 degrees from 180 degrees:
C = 180 - 38 = 142 degrees.
Now, we can find sin(B) using the following equation:
sin(B) = sin(180 - A - C) = sin(180 - 38 - 142) = sin(0) = 0.
Since sin(B) is 0, the length of side b (x) is also 0.
Therefore, the value of x is 0 in this case.