Question

find exact values or expressions for sin a, cos a, and tan a. see example 1. 1. 2. 3. 4.

Explanation:

1.

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin A=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos A = \frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan A=\frac{\text{opposite}}{\text{adjacent}}$.
For the first triangle with opposite side to angle $A$ of length $21$, adjacent side of length $20$, and hypotenuse of length $29$:
$\sin A=\frac{21}{29}$, $\cos A=\frac{20}{29}$, $\tan A=\frac{21}{20}$
2.
For the second triangle with opposite side to angle $A$ of length $45$, adjacent side of length $28$, and hypotenuse of length $53$:

Step1: Calculate sine

$\sin A=\frac{45}{53}$

Step2: Calculate cosine

$\cos A=\frac{28}{53}$

Step3: Calculate tangent

$\tan A=\frac{45}{28}$
3.
For the third triangle with opposite side to angle $A$ of length $n$, adjacent side of length $m$, and hypotenuse of length $p$:

Step1: Calculate sine

$\sin A=\frac{n}{p}$

Step2: Calculate cosine

$\cos A=\frac{m}{p}$

Step3: Calculate tangent

$\tan A=\frac{n}{m}$
4.
For the fourth triangle with opposite side to angle $A$ of length $k$, adjacent side of length $y$, and hypotenuse of length $z$:

Step1: Calculate sine

$\sin A=\frac{k}{z}$

Step2: Calculate cosine

$\cos A=\frac{y}{z}$

Step3: Calculate tangent

$\tan A=\frac{k}{y}$

Answer:

1. $\sin A=\frac{21}{29}$, $\cos A=\frac{20}{29}$, $\tan A=\frac{21}{20}$
2. $\sin A=\frac{45}{53}$, $\cos A=\frac{28}{53}$, $\tan A=\frac{45}{28}$
3. $\sin A=\frac{n}{p}$, $\cos A=\frac{m}{p}$, $\tan A=\frac{n}{m}$
4. $\sin A=\frac{k}{z}$, $\cos A=\frac{y}{z}$, $\tan A=\frac{k}{y}$