Subjects trigonometry

Find Angle Y F6230F

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We need to find the angle $y$ in a right triangle where the side opposite to $y$ is 19 and the adjacent side is 27. 2. **Formula used:** To find an angle in a right triangle when opposite and adjacent sides are known, use the tangent function: $$\tan(y) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** $$\tan(y) = \frac{19}{27}$$ 4. **Calculate the ratio:** $$\tan(y) = 0.7037$$ 5. **Find the angle $y$ by taking the arctangent:** $$y = \tan^{-1}(0.7037)$$ 6. **Evaluate using a calculator:** $$y \approx 35.1^\circ$$ 7. **Round to the nearest degree:** $$y \approx 35^\circ$$ **Final answer:** $y = 35^\circ$