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In a right triangle ABC with a right angle at A and angle B measuring 30 degrees, if BC is equal to √3, what is the length of side AC?

User Druckles
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Final answer:

In a right triangle ABC with a 30-degree angle at B and hypotenuse BC equal to √3, using the properties of a 30-60-90 triangle, the length of side AC is found to be 3/2 units.

Step-by-step explanation:

To determine the length of side AC in right triangle ABC with a right angle at A and angle B measuring 30 degrees, we use the properties of a 30-60-90 triangle which tell us that the side opposite the 30-degree angle (AB) is half the length of the hypotenuse (BC), and the side opposite the 60-degree angle (AC) is the length of the side opposite the 30-degree angle times the square root of three (√3).

Since BC is given to be equal to √3 (the hypotenuse), side AB would be half of BC, which is √3/2. To find the length of AC, we can apply the property of a 30-60-90 triangle which gives us AC = AB times the √3. If AB is √3/2, then AC is (√3/2) × √3 which simplifies to 3/2. Therefore, the length of side AC is 3/2 units.