A bird is perched on the top of a building that is 13 feet tall. You spot the bird as you’re walking across the street. If you are 6 feet tall and the diagonal distance from you to the bird is 26 feet, what is the angle of elevation you are using to look at the bird? Use the inverse of sine to find your answer and round to the nearest whole degree.(1 point)

Question

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Answer 1

To find the angle of elevation from your eyes to the bird, we can use some basic trigonometry. The relevant height difference and distance creates a right triangle.

1. Determine the height difference:

   • The height of the bird is 13 feet.
   • Your height is 6 feet.
   • The height difference is: \[ \text{Height difference} = 13 \text{ feet} - 6 \text{ feet} = 7 \text{ feet} \]

2. Identify the diagonal distance:

   • The diagonal distance (hypotenuse of the right triangle) to the bird is 26 feet.

3. Use the sine function: The sine of the angle of elevation (let’s call it \( \theta \)) can be defined as: \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\text{height difference}}{\text{diagonal distance}} = \frac{7}{26} \]

4. Calculate the sine value: \[ \sin(\theta) = \frac{7}{26} \approx 0.2692 \]

5. Find the angle using the inverse sine function: \[ \theta = \sin^{-1}(0.2692) \]

Using a calculator to compute this: \[ \theta \approx 15.7 \text{ degrees} \]

6. Round to the nearest whole degree: Therefore, the angle of elevation is approximately: \[ \theta \approx 16 \text{ degrees} \]

Thus, the angle of elevation you are using to look at the bird is 16°.