Question

in a right triangle, one angle measures 25°, and the opposite side is 5 units. find the length of the side adjacent to the 25° angle.

Explanation:

Step1: Recall tangent ratio definition

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Rearrange for adjacent side

$\text{adjacent} = \frac{\text{opposite}}{\tan(\theta)}$

Step3: Substitute given values

$\text{adjacent} = \frac{5}{\tan(25^\circ)}$

Step4: Calculate numerical value

$\tan(25^\circ) \approx 0.4663$, so $\text{adjacent} \approx \frac{5}{0.4663} \approx 10.72$

Answer:

Approximately 10.72 units