Question

in the given figure, the hypotenuse is 64. what is the cos x? note: figure not drawn to scale a. √3/2 b. 1/2 c. 2√3/3 d. 2

Explanation:

Step1: Recall cosine definition

The cosine of an angle in a right - triangle is defined as $\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Identify adjacent and hypotenuse

Assume the adjacent side to angle $x$ is $a$ and the hypotenuse is $h = 4$. If we consider a 30 - 60 - 90 triangle where the side adjacent to the 60 - degree angle (assuming $x = 60^{\circ}$) and hypotenuse relationship is used. In a 30 - 60 - 90 triangle, if the hypotenuse $h = 4$, and the side adjacent to the 60 - degree angle is 2. So $\cos x=\frac{2}{4}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$