Subjects trigonometry

Angle From Sides 75Ee19

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1. **State the problem:** We need to find the measure of the angle labeled with a question mark (?) in a right triangle where the opposite side length is 70 and the adjacent side length is 39. 2. **Formula used:** To find an angle in a right triangle when opposite and adjacent sides are known, use the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** $$\tan(\theta) = \frac{70}{39}$$ 4. **Calculate the ratio:** $$\tan(\theta) = 1.79487$$ 5. **Find the angle:** Use the inverse tangent (arctan) to find $\theta$: $$\theta = \tan^{-1}(1.79487)$$ 6. **Evaluate the angle:** $$\theta \approx 60.9^\circ$$ 7. **Conclusion:** The angle labeled with ? is approximately $60.9^\circ$.