a Examining the diagram, we see that this is a right triangle where one of the non-right angle is 30^(∘). This fits the description of a 30-60-90 triangle. In such a triangle, the hypotenuse is always twice as long as the shorter leg, and the longer leg is sqrt(3) times as long as the shorter leg. Let's illustrate this.
In the given triangle, the hypotenuse is x. Therefore, we get the following equation.
x=2a
Since we know the value of a in the given triangle is 12, we can determine x.
b Examining the diagram, we can see that the triangle has a 45^(∘)-angle and a right angle. This makes it a 45-45-90 triangle. In such a special triangle, the hypotenuse is always sqrt(2) times longer than its legs.
In the given triangle, the hypotenuse is 1. We get the following equation
asqrt(2)=1
Let's solve for a, which is the same as x in the given triangle.
