Question

What is the length of x in the diagram below?

A triangle with vertical bisector forms 2 triangles with a right angle. One triangle has a side length of 5 and another angle with a measure 45 degrees. Another triangle has a hypotenuse with length x and another angle with measure 30 degrees.
StartFraction 5 Over StartRoot 3 EndRoot
StartFraction 10 Over StartRoot 3 EndRoot EndFraction
5 StartRoot 3 EndRoot
10

Answer 1

The length of x is (10√3)/3.

Explanation:

Using the trigonometric ratios of a 30-60-90 triangle, we know that the side opposite the 30-degree angle is half the length of the hypotenuse. Therefore, we have:

x/2 = (5/√3)

Multiplying both sides by 2, we get:

x = 10/√3, which can be simplified to:

x = (10√3)/3

So the length of x is (10√3)/3.

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