Questions: What is the length of side AB? (Lesson 4-3)

What is the length of side AB? (Lesson 4-3)
Transcript text: 6. What is the length of side $A B$ ? (Lesson 4-3)
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Solution

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Solution Steps

Step 1: Identify the given information

We are given a 30-60-90 triangle. Side AC has a length of 6, angle C is 30°, angle A is 90° and angle B is 60°. We want to find the length of side AB.

Step 2: Relate sides in a 30-60-90 triangle

In a 30-60-90 triangle, the side opposite the 30° angle (AC) is considered the short leg. The side opposite the 60° angle (AB) is the long leg. The side opposite the 90° angle (BC) is the hypotenuse. The ratio of the sides is short leg : long leg : hypotenuse = x : x√3 : 2x.

Step 3: Calculate AB

Since AC = 6, this corresponds to the short leg, which is represented by x. Therefore, x = 6. The long leg (AB) is represented by x√3. Substituting x = 6, we find AB = 6√3.

Final Answer

6√3

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