Question

select the correct answer.

in \\(\delta abc\\), which trigonometric ratio equals \\(\frac{3}{2}\\)?

Explanation:

Identify the given side lengths

We are given a right-angled triangle \(\triangle ABC\) with:

• Angle \(A = 90^\circ\)
• Side \(AC = 2\) (opposite to angle \(B\))
• Side \(AB = 3\) (opposite to angle \(C\))
• Hypotenuse \(BC = 3.61\)

Analyze the target ratio

We need to find which trigonometric ratio equals \(\frac{3}{2}\).
Let's look at the ratio:

$$\frac{\text{Side of length } 3}{\text{Side of length } 2} = \frac{AB}{AC}$$

Evaluate ratios for angle B

For angle \(B\):

• Opposite side is \(AC = 2\)
• Adjacent side is \(AB = 3\)
• \(\tan(B) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{2}{3}\)

Evaluate ratios for angle C

For angle \(C\):

• Opposite side is \(AB = 3\)
• Adjacent side is \(AC = 2\)
• \(\tan(C) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{3}{2}\)

Match with the correct option

The trigonometric ratio that equals \(\frac{3}{2}\) is \(\tan(C)\).

Answer:

• \(\tan(C)\) (Correct answer)
• \(\tan(B)\)
• \(\sin(C)\)
• \(\cos(B)\)