Question

in △def, m∠d = 30 and m∠e = 60. is overline{ef} or overline{df} longer? after you enter your answer press go.

Explanation:

Step1: Find the measure of angle \(F\)

In a triangle, the sum of interior angles is \(180^{\circ}\). Given \(m\angle D = 30^{\circ}\) and \(m\angle E=60^{\circ}\), then \(m\angle F=180-(30 + 60)=90^{\circ}\).

Step2: Apply the side - angle relationship in a triangle

In a triangle, the larger angle is opposite the longer side.

• The side opposite \(\angle D = 30^{\circ}\) is \(EF\).
• The side opposite \(\angle E = 60^{\circ}\) is \(DF\).

Since \(60^{\circ}>30^{\circ}\), by the side - angle relationship (\(a/sinA=b/sinB = c/sinC\) in the law of sines, or simply the larger - angle - opposite - longer - side rule in a triangle), the side opposite the larger angle is longer.

Answer:

\(\overline{DF}\) is longer.