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.

Answer 1

To find the angle of elevation to the bird, we can use the given information to create a right triangle.

1. Determine the height difference: The bird is perched at a height of 13 feet, and you are 6 feet tall. Therefore, the height difference between the bird and your eyes is: \[ \text{Height difference} = 13 \text{ feet} - 6 \text{ feet} = 7 \text{ feet} \]

2. Identify the components: In our right triangle:

   • The height from your eye level to the bird (opposite side) is 7 feet.
   • The diagonal distance from you to the bird (hypotenuse) is 26 feet.

3. Use the sine function: The angle of elevation \(\theta\) can be calculated using the sine function: \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{7}{26} \]

4. Calculate the angle using the inverse sine: We can find the angle \(\theta\) by taking the inverse sine (arcsin): \[ \theta = \arcsin\left(\frac{7}{26}\right) \]

5. Calculate \(\theta\): Using a calculator: \[ \theta \approx \arcsin(0.2692) \approx 15.71^\circ \]

6. Round to the nearest whole degree: \[ \theta \approx 16^\circ \]

Therefore, the angle of elevation you are using to look at the bird is approximately 16 degrees.