Question

given the following triangle, \\(cos \theta =\\) ____ .

the triangle is a right triangle with legs 3 and 4, hypotenuse 5, and angle \\(\theta\\) opposite the leg of length 3, adjacent to the leg of length 4.

options:
\\(\frac{4}{3}\\)
\\(\frac{4}{5}\\)
\\(\frac{5}{3}\\)
\\(\frac{3}{4}\\)

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos\theta=\frac{\text{adjacent side to } \theta}{\text{hypotenuse}}$.

Step2: Identify sides

For angle $\theta$, adjacent side is $4$, hypotenuse is $5$.

Step3: Calculate $\cos\theta$

$\cos\theta=\frac{4}{5}$.

Answer:

$\frac{4}{5}$ (corresponding to the option "4/5")