- The problem involves finding the angle of depression from the top of a 70 ft tall cliff to the edge of water that is 50 ft away horizontally.
- This forms a right triangle where the height of the cliff (70 ft) is the opposite side and the horizontal distance to the water (50 ft) is the adjacent side relative to the angle of depression.
- The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side: tan(θ) = opposite / adjacent.
- Therefore, tan(x) = 70 / 50.
- To find the angle x, take the inverse tangent (arctangent) of this ratio: x = arctan(70/50).
- Calculating this gives x ≈ 54.46 degrees.
- The provided solution of x = 4° is incorrect because it likely resulted from a calculation error or misapplication of the formula (e.g., using arctan(70/50) but interpreting the result incorrectly or using a wrong calculator mode).
Parent Tip: Review the logic above to help your child master the concept of trig ratios word problems worksheet.
