Question

Solve for A and B using special right triangles
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Answer 1

a = 10

b = 5

Explanation:

A 30-60-90 triangle is a right triangle where the interior angles measure 30°, 60° and 90° and the sides are in the ratio 1 : √3 : 2.

The formula for the ratio of the sides is x : x√3 : 2x where:

• x = the shortest side opposite the 30° angle.
• x√3 = the side opposite the 60° angle.
• 2x = the longest side (hypotenuse) opposite the right angle.

From inspection of the given triangle, the measure of the side opposite the 30° angle is "b", the side opposite the 60° angle is 5√3, and the hypotenuse is "a". Therefore:

• x = b
• x√3 = 5√3
• 2x = a

If x√3 = 5√3, then x = 5. Therefore:

• b = x = 5
• a = 2x = 10