1. **State the problem:** A goldfinch is flying 13 metres away from a bird box on top of a pole. The angle of depression from the goldfinch to the base of the pole is 32°. We need to find the distance between the goldfinch and the base of the pole. 2. **Understand the setup:** The goldfinch, the base of the pole, and the bird box form a right triangle. The hypotenuse is the line from the goldfinch to the bird box (13 m). The angle of depression (32°) is the angle between the line of sight and the horizontal ground. 3. **Identify the sides:** - Hypotenuse ($c$) = 13 m - Angle of depression = 32° - Distance from goldfinch to base of pole = adjacent side ($b$) 4. **Formula used:** In a right triangle, cosine of an angle is adjacent over hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 5. **Apply the formula:** $$\cos(32^\circ) = \frac{b}{13}$$ 6. **Solve for $b$:** $$b = 13 \times \cos(32^\circ)$$ 7. **Calculate the value:** $$b = 13 \times 0.8480 = 11.024$$ 8. **Round to 2 decimal places:** $$b \approx 11.02$$ **Final answer:** The distance between the goldfinch and the base of the pole is approximately **11.02 metres**.