Question

finding missing measurements
consider the triangle.
angle ( a = 60 ^ { circ } )
angle ( b = 30 ^ { circ } )
angle ( c = 90 ^ { circ } )
( a b = 10 )
( a c = 5 )
( b c = )

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(ABC\) with \(\angle C = 90^{\circ}\), by the Pythagorean theorem \(AB^{2}=AC^{2}+BC^{2}\).
Given \(AB = 10\) and \(AC = 5\), we can rewrite the formula as \(BC=\sqrt{AB^{2}-AC^{2}}\).

Step2: Substitute values

Substitute \(AB = 10\) and \(AC = 5\) into the formula:

$$
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$$

Answer:

\(5\sqrt{3}\)