ANSWERS
a.
b. sin(θ) = 21/29
c. tan(θ) = 21/20
EXPLANATION
For any right triangle the trigonometric ratios are:
[tex]\cos \theta=\frac{\text{adjacent}}{\text{ hypotenuse}}[/tex][tex]\sin \theta=\frac{\text{opposite}}{\text{ hypotenuse}}[/tex][tex]\tan \theta=\frac{\sin \theta}{\cos \theta}=\frac{\text{ opposite}}{\text{ adjacent}}[/tex]
We know the hypotenuse and the adjacent, we want to know the opposite. We can find it using the Pythagorean theorem:
[tex]\begin{gathered} h^2=(\text{adjacent)}^2+(\text{opposite)}^2 \\ 29^2=20^2+(\text{opposite)}^2 \\ \text{opposite}=\sqrt[]{29^2-20^2} \\ \text{opposite}=\sqrt[]{441} \\ \text{opposite}=21 \end{gathered}[/tex]
The sine of the angle is:
[tex]\sin \theta=\frac{21}{29}[/tex]
The tangent is:
[tex]\tan \theta=\frac{21}{20}[/tex]
