Question

fall 2025 geometry b wwva right triangle relationships and trigonometry which is the best approximation for the measure of angle abc? 27.7° 31.7° 58.3° 62.3°

Explanation:

Step1: Identify trigonometric - ratio

In right - triangle \(ABC\) with right - angle at \(C\), we use the tangent function. \(\tan\angle ABC=\frac{AC}{BC}\). Here, \(AC = 10.5\) cm and \(BC = 20\) cm. So, \(\tan x=\frac{10.5}{20}=0.525\).

Step2: Find the angle

We know that if \(\tan x = 0.525\), then \(x=\arctan(0.525)\). Using a calculator, \(x=\arctan(0.525)\approx 27.7^{\circ}\).

Answer:

\(27.7^{\circ}\)