Question

if you know the sides of a triangle are 18, 36, and 18√3, what are the three angles in the triangle? type your answer here

Explanation:

Step1: Identify triangle type (30-60-90)

Check side ratios: \( \frac{18}{36} = \frac{1}{2} \), \( \frac{18\sqrt{3}}{36} = \frac{\sqrt{3}}{2} \). Matches 30-60-90 triangle (sides \( x, 2x, x\sqrt{3} \)).

Step2: Assign angles

Shortest side (\( 18 \)) opposite \( 30^\circ \), side \( 18\sqrt{3} \) opposite \( 60^\circ \), longest side (\( 36 \)) opposite \( 90^\circ \).

Answer:

The three angles are \( 30^\circ \), \( 60^\circ \), and \( 90^\circ \).