Question

19 in right triangle jkl in the diagram below, kl = 7, jk = 24, jl = 25, and ∠k = 90°. which statement is not true? 1) tan l = 24/7 2) cos l = 24/25 3) tan j = 7/24 4) sin j = 7/25

Explanation:

Step1: Recall the trigonometric ratios

In a right - triangle, for an angle \(\theta\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\)

Step2: Analyze \(\tan L\)

For \(\angle L\), the opposite side to \(\angle L\) is \(JK = 24\) and the adjacent side is \(KL=7\). So, \(\tan L=\frac{JK}{KL}=\frac{24}{7}\)

Step3: Analyze \(\cos L\)

For \(\angle L\), the adjacent side is \(KL = 7\) and the hypotenuse is \(JL = 25\). So, \(\cos L=\frac{KL}{JL}=\frac{7}{25}
eq\frac{24}{25}\)

Step4: Analyze \(\tan J\)

For \(\angle J\), the opposite side is \(KL = 7\) and the adjacent side is \(JK = 24\). So, \(\tan J=\frac{KL}{JK}=\frac{7}{24}\)

Step5: Analyze \(\sin J\)

For \(\angle J\), the opposite side is \(KL = 7\) and the hypotenuse is \(JL = 25\). So, \(\sin J=\frac{KL}{JL}=\frac{7}{25}\)

Answer:

1. \(\cos L=\frac{24}{25}\)