Question

find d.
triangle with right angle, 60° angle, 30° angle, hypotenuse 30 m, side d
write your answer in simplest radical form.
blank meters
radical symbol button

Explanation:

Step1: Identify Triangle Type

The triangle is right - angled (one right angle) with angles \(30^{\circ}\), \(60^{\circ}\), and \(90^{\circ}\), so it's a 30 - 60 - 90 triangle. In a 30 - 60 - 90 triangle, the sides are in the ratio \(1:\sqrt{3}:2\), where the side opposite \(30^{\circ}\) is the shortest side (let's call it \(x\)), the side opposite \(60^{\circ}\) is \(x\sqrt{3}\), and the hypotenuse is \(2x\).
Here, the hypotenuse (the side opposite the right angle) has length \(30\) m. The side \(d\) is opposite the \(60^{\circ}\) angle.

Step2: Relate Sides in 30 - 60 - 90 Triangle

Let the side opposite \(30^{\circ}\) be \(x\). Then the hypotenuse \(h = 2x\). We know \(h=30\) m, so \(2x = 30\), which gives \(x = 15\) m.
The side opposite \(60^{\circ}\) (which is \(d\)) is \(x\sqrt{3}\). Substituting \(x = 15\) into this formula, we get \(d=15\sqrt{3}\) m.

Answer:

\(15\sqrt{3}\)