Question

4 - 6 practice
geometry (s1 p01 rm h218) sharp, jeffrey / unit 4 - right triangle trigonometry / lesson 4 - 6 working with trigono

1. find the length of each leg

qp =
qr =
(lesson 4 - 3)

Explanation:

Step1: Use the property of 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, if the hypotenuse \(c = 4\), and the sides are in the ratio \(1:\sqrt{3}:2\). The side opposite the 30° angle is the shortest side. Let the side opposite 30° angle be \(QP\), and the side opposite 60° angle be \(QR\).
The formula for the sides of a 30 - 60 - 90 triangle: if the hypotenuse \(c\), then the side opposite 30° (\(a\)) is \(a=\frac{c}{2}\), and the side opposite 60° (\(b\)) is \(b = \frac{c\sqrt{3}}{2}\)

Step2: Calculate \(QP\)

Since \(QP\) is opposite the 30° angle and \(c = 4\), using \(a=\frac{c}{2}\), we have \(QP=\frac{4}{2}=2\)

Step3: Calculate \(QR\)

Since \(QR\) is opposite the 60° angle and \(c = 4\), using \(b=\frac{c\sqrt{3}}{2}\), we have \(QR=\frac{4\sqrt{3}}{2}=2\sqrt{3}\)

Answer:

\(QP = 2\), \(QR=2\sqrt{3}\)