Question

18 in right triangle abc shown below, ac = 12, bc = 16, and ab = 20. which equation is not correct? 1) cos a = \frac{12}{20} 2) tan a = \frac{16}{12} 3) sin b = \frac{12}{20} 4) tan b = \frac{16}{20}

Explanation:

Step1: Recall trigonometric ratios

• $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Analyze $\cos A$

• For $\angle A$, adjacent side is $AC = 12$, hypotenuse is $AB=20$. So $\cos A=\frac{AC}{AB}=\frac{12}{20}$

Step3: Analyze $\tan A$

• For $\angle A$, opposite side is $BC = 16$, adjacent side is $AC = 12$. So $\tan A=\frac{BC}{AC}=\frac{16}{12}$

Step4: Analyze $\sin B$

• For $\angle B$, opposite side is $AC = 12$, hypotenuse is $AB = 20$. So $\sin B=\frac{AC}{AB}=\frac{12}{20}$

Step5: Analyze $\tan B$

• For $\angle B$, opposite side is $AC = 12$, adjacent side is $BC = 16$. So $\tan B=\frac{AC}{BC}=\frac{12}{16}

eq\frac{16}{20}$

Answer:

1. $\tan B=\frac{16}{20}$