Question

what is the length of side x? triangle image with right angle, base 14 cm, angle 28° at the bases end, side x opposite to the 28° angle? wait, no, x is the vertical leg, base is 14 cm (adjacent to 28°), x is opposite? wait, right triangle: right angle, one angle 28°, base (adjacent to 28°) is 14 cm, x is the opposite leg? wait, no, maybe x is the opposite? wait, the triangle: right angle, angle 28° at the end of the base (14 cm), so the base is adjacent to 28°, x is the opposite leg (vertical). so we can use tangent: tan(28°) = x / 14, so x = 14 tan(28°). or maybe cotangent? wait, no: in a right triangle, tan(theta) = opposite / adjacent. so theta is 28°, opposite is x, adjacent is 14. so x = 14 tan(28°). lets calculate tan(28°) ≈ 0.5317, so 14 * 0.5317 ≈ 7.44 cm. the options are 7 cm, 26.33 cm, 6.57 cm, 7.44 cm. so the question is: what is the length of side x? with options 7 cm, 26.33 cm, 6.57 cm, 7.44 cm.

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 28^{\circ}\), the adjacent side \(a = 14\ \text{cm}\), and the opposite side is \(x\). So, \(\tan(28^{\circ})=\frac{x}{14}\).

Step2: Solve for \(x\)

We know that \(\tan(28^{\circ})\approx0.5317\). Then \(x = 14\times\tan(28^{\circ})\). Substituting the value of \(\tan(28^{\circ})\), we get \(x=14\times0.5317 = 7.4438\approx7.44\ \text{cm}\).

Answer:

\(7.44\ \text{cm}\)