Question

question 6 (multiple choice worth 1 points) (05.01r mc) in △jkl, what is the length of segment kl? 11.5 23√2 46 23√3

Explanation:

Step1: Find the measure of angle \( L \)

In a right - triangle \( \triangle JKL\) with \( \angle K = 90^{\circ}\) and \( \angle J=60^{\circ}\), using the angle - sum property of a triangle (\( \angle K+\angle J+\angle L = 180^{\circ}\)), we get \( \angle L=180^{\circ}-\angle K - \angle J=180^{\circ}-90^{\circ}-60^{\circ}=30^{\circ}\).

Step2: Use the trigonometric ratio \(\tan\)

We know that \(\tan J=\frac{KL}{KJ}\). Since \(J = 60^{\circ}\) and \(KJ = 23\), and \(\tan60^{\circ}=\sqrt{3}\).
From the formula \(\tan J=\frac{KL}{KJ}\), we can solve for \(KL\) by multiplying both sides by \(KJ\). So \(KL=KJ\times\tan J\).
Substitute \(KJ = 23\) and \(\tan60^{\circ}=\sqrt{3}\) into the equation: \(KL = 23\times\sqrt{3}\).

Answer:

\(23\sqrt{3}\)