Ok, so im brand new at trigonometry. If i have a right triangle with an acute angle of 30° an opposite side of 4 and a hypotenuse of x how do ii find x
sin 30 = opposite / hypotenuse = 1/2
4/x = 1/2
x = 8
by the way:
If it is a right triangle one angle is 90 degrees
the sum of angles is 180
so
90 + 30 + last angle = 180
the last angle is 60
To find the length of the hypotenuse (x) of a right triangle given an acute angle of 30° and an opposite side of 4, you can use the trigonometric function known as the sine (sin).
The sine of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In this case, the sine of 30° is equal to the length of the opposite side (4) divided by the length of the hypotenuse (x). So, we have:
sin(30°) = 4 / x
To solve for x, you can cross-multiply and isolate x:
x * sin(30°) = 4
To find x, you need to know the value of sin(30°). Since trigonometric values can be found using special triangles or calculators, you can use the special triangle for a 30°-60°-90° triangle.
In a 30°-60°-90° triangle, the ratio between the length of the hypotenuse and the length of the shorter leg is equal to √3:1. Since the hypotenuse is denoted by x, and the side opposite the 30° angle is denoted by 4, you can write:
x / 4 = √3 / 1
To solve for x, you can cross-multiply and simplify:
x = 4 * √3
So, the length of the hypotenuse (x) is 4 times the square root of 3 (approx. 6.928).