Question

7 in right triangle lmn shown below, m∠m = 90°, mn = 12 and lm = 16. the ratio of cos n is 1) 12/20 2) 16/20 3) 12/16 4) 16/12

Explanation:

Step1: Find the hypotenuse \(LN\) using Pythagorean theorem

$$LN=\sqrt{LM^{2}+MN^{2}}=\sqrt{16^{2}+12^{2}}=\sqrt{256 + 144}=\sqrt{400}=20$$

Step2: Recall the cosine formula for a right - triangle

In a right - triangle \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle N\), the adjacent side to \(\angle N\) is \(MN = 12\) and the hypotenuse is \(LN=20\). So \(\cos N=\frac{MN}{LN}\)
$$\cos N=\frac{12}{20}$$

Answer:

1. \(\frac{12}{20}\)