Question

7.

8.

9.

x=

x=

x=

y=

y=

y=

Explanation:

Step1: Solve problem 7

In a \(30 - 60-90\) triangle, the sides are in the ratio \(1:\sqrt{3}:2\). The hypotenuse is \(46\). The side opposite \(30^{\circ}\) (\(y\)) is half of the hypotenuse.
\(y=\frac{46}{2}=23\)
The side opposite \(60^{\circ}\) (\(x\)) is \(y\sqrt{3}\).
\(x = 23\sqrt{3}\)

Step2: Solve problem 8

In a \(30 - 60-90\) triangle, if the side opposite \(60^{\circ}\) is \(20\). Let the side opposite \(30^{\circ}\) be \(y\). Then \(\tan60^{\circ}=\frac{20}{y}\), \(y=\frac{20}{\sqrt{3}}=\frac{20\sqrt{3}}{3}\). The hypotenuse \(x\) is \(2y\).
\(x=\frac{40\sqrt{3}}{3}\)

Step3: Solve problem 9

In a \(30 - 60-90\) triangle, if the side opposite \(60^{\circ}\) is \(9\sqrt{3}\). Let the side opposite \(30^{\circ}\) be \(x\). Then \(\tan60^{\circ}=\frac{9\sqrt{3}}{x}\), \(x = 9\). The hypotenuse \(y\) is \(2x\).
\(y = 18\)

Answer:

1. \(x = 23\sqrt{3}\), \(y=23\)
2. \(x=\frac{40\sqrt{3}}{3}\), \(y=\frac{20\sqrt{3}}{3}\)
3. \(x = 9\), \(y = 18\)