Question

1. what are the values of x & y? image of a right triangle with angle 30°, angle 60°, hypotenuse 18, leg y, leg x; and another right triangle with angle 30°, angle 60°, hypotenuse 14, leg y, leg x 5) same as above but hypotenuse 14

Explanation:

Problem 4:

Step1: Identify triangle type

It's a 30-60-90 right triangle. In such a triangle, the sides are in the ratio \(1 : \sqrt{3} : 2\), where the side opposite \(30^\circ\) is the shortest (\(y\)), opposite \(60^\circ\) is \(x\), and hypotenuse is \(18\).

Step2: Find \(y\) (opposite \(30^\circ\))

In 30-60-90 triangle, hypotenuse \(= 2 \times\) shortest side. So \(y=\frac{18}{2}=9\).

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

The side opposite \(60^\circ\) is \(\sqrt{3}\) times the shortest side. So \(x = y\sqrt{3}=9\sqrt{3}\).

Step1: Identify triangle type

It's a 30-60-90 right triangle. Hypotenuse is \(14\), side opposite \(30^\circ\) is \(y\), opposite \(60^\circ\) is \(x\).

Step2: Find \(y\) (opposite \(30^\circ\))

In 30-60-90 triangle, \(y=\frac{\text{hypotenuse}}{2}=\frac{14}{2}=7\).

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

Side opposite \(60^\circ\) is \(y\sqrt{3}\), so \(x = 7\sqrt{3}\).

Answer:

\(x = 9\sqrt{3}\), \(y = 9\)

Problem 5: