Question

quiz 2.3.1 - sine, cosine, and tangent
12
20
a
a. tan a
b. sin a
c. cos a

1. 4/3
2. 4/5

Explanation:

Step1: Find the adjacent - side length

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$. Let the adjacent - side to angle $A$ be $x$. Given the hypotenuse $c = 20$ and the opposite - side $b = 12$. Then $x=\sqrt{20^{2}-12^{2}}=\sqrt{400 - 144}=\sqrt{256}=16$.

Step2: Calculate $\tan A$

The formula for tangent is $\tan A=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\text{opposite}=12$ and $\text{adjacent}=16$, so $\tan A=\frac{12}{16}=\frac{3}{4}$.

Step3: Calculate $\sin A$

The formula for sine is $\sin A=\frac{\text{opposite}}{\text{hypotenuse}}$. So $\sin A=\frac{12}{20}=\frac{3}{5}$.

Step4: Calculate $\cos A$

The formula for cosine is $\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}$. So $\cos A=\frac{16}{20}=\frac{4}{5}$.

Answer:

a. $\tan A=\frac{3}{4}$
b. $\sin A=\frac{3}{5}$
c. $\cos A=\frac{4}{5}$