Question

find the following ratios for the angle a.
\frac{opposite side}{adjacent side} =
\frac{opposite side}{hypotenuse} =

Explanation:

Step1: Calculate the hypotenuse

Use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 35\), \(b=12\).
\(c=\sqrt{35^{2}+12^{2}}=\sqrt{1225 + 144}=\sqrt{1369}=37\)

Step2: Find \(\frac{\text{OPPOSITE SIDE}}{\text{ADJACENT SIDE}}\)

For angle \(A\), the opposite side is \(BC = 12\), the adjacent side is \(AC=35\).
\(\frac{\text{OPPOSITE SIDE}}{\text{ADJACENT SIDE}}=\frac{12}{35}\)

Step3: Find \(\frac{\text{OPPOSITE SIDE}}{\text{HYPOTENUSE}}\)

For angle \(A\), the opposite side is \(BC = 12\), the hypotenuse is \(AB = 37\).
\(\frac{\text{OPPOSITE SIDE}}{\text{HYPOTENUSE}}=\frac{12}{37}\)

Answer:

\(\frac{12}{35}\), \(\frac{12}{37}\)