Question

question 47 of 50
the value of x is:
triangle with right angle, 30° angle, hypotenuse 14, leg x
options: (7sqrt{3}), (7sqrt{2}), 7, 14, (14sqrt{3})

Explanation:

Step1: Identify triangle type

It's a right - triangle with a \(30^{\circ}\) angle, so it's a 30 - 60 - 90 triangle. In a 30 - 60 - 90 triangle, the sides are in the ratio \(1:\sqrt{3}:2\) (opposite \(30^{\circ}\), \(60^{\circ}\), hypotenuse respectively). The hypotenuse here is 14.

Step2: Find the side opposite \(30^{\circ}\)

The side opposite \(30^{\circ}\) is half the hypotenuse. So the side opposite \(30^{\circ}\) is \(\frac{14}{2}=7\).

Step3: Find \(x\) (opposite \(60^{\circ}\))

The side opposite \(60^{\circ}\) (which is \(x\)) is \(\sqrt{3}\) times the side opposite \(30^{\circ}\). So \(x = 7\sqrt{3}\).

Answer:

\(7\sqrt{3}\) (corresponding to the option with \(7\sqrt{3}\))