Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the 30. 60. 90 Triangle Theorem to find the answer.
5, x, y 50
Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
Based on the given information, we can determine that the triangle is a 30-60-90 triangle.
In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows:
- The length of the side opposite the 30-degree angle is half the length of the hypotenuse.
- The length of the side opposite the 60-degree angle is the product of the length of the hypotenuse and √3.
- The length of the hypotenuse is twice the length of the side opposite the 30-degree angle.
Given the triangle with sides 5, x, and y, we can determine the missing side lengths using the 30-60-90 triangle theorem.
First, we know that the side opposite the 30-degree angle is half the length of the hypotenuse. So, we have:
x/5 = 1/2
To solve for x, we can cross multiply:
2x = 5
Dividing both sides by 2, we find:
x = 5/2
Therefore, the value of x is 5/2.