aing Classkick L52-Rt Angle Ting (Th) Question 11 of 25 (1 point) । Question Aftempt 1 of 5 First use the Pythagorean theorem to find the exact length of the missing side of the right triangle. Then find the exact values of the six trigonometric functions for the angle \( \theta \) opposite the shortest side. Leg \( =4 \sqrt{23} \mathrm{~m} \), Hypotenuse \( =6 \sqrt{13} \mathrm{~m} \) Part 1 of 2 Hypotenuse \( =6 \sqrt{13} \mathrm{~m} \), Leg \( =4 \sqrt{23} \mathrm{~m} \), Leg \( =10 \mathrm{~m} \).

To find the missing side using the Pythagorean theorem, recall the formula \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse. Here, you have \(c = 6\sqrt{13}\) and \(a = 4\sqrt{23}\). Thus, \(b^2 = (6\sqrt{13})^2 - (4\sqrt{23})^2\). Calculate this to find \(b = 10\) m. Now, for the six trigonometric functions of angle \( \theta \), where \( \theta \) is opposite the shortest leg (10 m): 1. sin(θ) = opposite/hypotenuse = \(10/6\sqrt{13}\) 2. cos(θ) = adjacent/hypotenuse = \(4\sqrt{23}/6\sqrt{13}\) 3. tan(θ) = opposite/adjacent = \(10/(4\sqrt{23})\) 4. csc(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), cot(θ) = 1/tan(θ). Simplify these for the exact trigonometric values! Enjoy the journey into angles!