Question

Find the length of side x in simplest radical form with a rational denominator

Answer 1

x = 9√3

Explanation:

The given triangle is a 30-60-90 triangle.

A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio of 1 : √3 : 2.

Therefore, the formula for the sides is a : a√3 : 2a where:

• a is the side opposite the 30° angle.
• a√3 is the side opposite the 60° angle.
• 2a is the side opposite the right angle.

From inspection of the triangle, the side opposite the 30° angle is:

• a = 9

Therefore,

• 9√3 is the side opposite the 60° angle.
• 18 is the side opposite the right angle (hypotenuse).

Therefore, the length of side x in simplest radical form is:

• x = 9√3

Answer 2

• x = 9√3

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Use tangent to find the missing leg x:

• tangent = opposite leg / adjacent leg

• tan 60° = x / 9 tan 60° = √3
• √3 = x / 9 multiply both sides by 9
• x = 9√3 answer