Question

given the diagram below, which of the following can be used to find x? diagram of a right triangle with right angle at the bottom left, horizontal leg 24, hypotenuse 25, angle at bottom right 27 degrees, vertical leg x options: - tan(27) = 24/x - tan(27) = x/24 - cos(27) = 25/x - sin(27) = 25/x

Explanation:

Step1: Recall Trigonometric Ratios

In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. The formula is $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify Sides Relative to 27°

For the 27° angle:

• The opposite side to 27° is \( x \).
• The adjacent side to 27° is 24.

Step3: Apply Tangent Ratio

Using the tangent ratio, $\tan(27^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{24}$.

Answer:

$\tan(27) = \frac{x}{24}$ (the second option)