Step-by-step explanation:
We are asked to find y, a missing side in a triangle.
1. Special Triangle Rules
This triangle is special. There is a 30-degree angle and a right angle or 90 degree angle, the unlabeled angle is 60 degrees. This is a 30-60-90 triangle so the sides are always in a specific relationship.
The side across from the 30-degree angle is a, the hypotenuse is 2a, and the side across from the 60-degree angle is √3 a.
y is across from the 30 degree angle, so it is equal to a. However, we have to find a. We are given one side that measures 6. It is the hypotenuse because it is across from the right angle. Therefore, it is equal to 2a.
2a= 6
a is being multiplied by 2. Divide both sides by 2 to solve for a.
2a/2= 6/2 a= 6/2 a=3
y is across from the 30-degree angle, so it is equal to a or 3.
2. Trigonometric Functions
We can also solve using the 3 main trigonometric functions.
sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacent
y is opposite the 30-degree angle and 6 is the hypotenuse, and we will use sine.
y is being divided by 6. The inverse operation of division is multiplication. Multiply both sides by 6 to solve for y.
The missing side, y , is equal to 3.
