Given the right traingle, let's solve for the following using trigonomteric ratio formula.
Thus, we have:
• sin Z:
Apply the trigonometric ratio formula for sine:
[tex]\sin Z=\frac{opposite}{hypotenuse}[/tex]Where:
Opposite side is the side opposite the given angle (Z) = XY = 36
Hypotenuse is the longest side of the traingle = XZ = 39
We have:
[tex]\begin{gathered} \sin Z=\frac{36}{39} \\ \\ \sin Z=0.9231 \end{gathered}[/tex]• cos Z:
Apply the trigonometric ratio formula for cosine:
[tex]\cos Z=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]Where:
Adjacent side is the side adjacent to the given angle (Z) = ZY = 15
Hypotenuse is the longest side of the triangle = XZ = 39
We have:
[tex]\begin{gathered} \cos Z=\frac{15}{39} \\ \\ \cos Z=0.3846 \end{gathered}[/tex]• tan Z:
Apply the trigonometric ratio formula for tan:
[tex]\tan Z=\frac{\text{opposite}}{\text{adjacent}}[/tex]Where:
Opposite side is the side opposite the given angle = XY = 36
Adjacent side is the side adjacent to angle Z = ZY = 15
We have:
[tex]\begin{gathered} \tan Z=\frac{36}{15} \\ \\ \tan Z=2.4 \end{gathered}[/tex]• sin X:
Apply the trigonometric ratio formula for sine:
[tex]\sin X=\frac{opposite}{hypotenuse}[/tex]Opposite side is the side opposite the given angle (X) = ZY=15
Hypotenuse is the longest side = XZ = 39
[tex]\begin{gathered} \sin X=\frac{15}{39} \\ \\ \sin X=0.3846 \end{gathered}[/tex]• cos X:
[tex]\begin{gathered} \cos X=\frac{adjacent}{\text{hypotenuse}} \\ \\ \cos X=\frac{36}{39} \\ \\ \cos X=0.9231 \end{gathered}[/tex]• tanX:
[tex]\begin{gathered} \tan X=\frac{\text{opposite}}{\text{adjacent}} \\ \\ \tan X=\frac{15}{36} \\ \\ \tan X=0.4167 \end{gathered}[/tex]ANSWER:
• sin Z = 0.9231
,• cos Z = 0.3846
,• tan Z = 2.4
,• sin X = 0.3846
,• cos X = 0.9231
,• tan X = 0.4167
