Question

Use the image to answer the question. Meekah is looking at a bird perched on top of a street light. Her line of sight, which is the diagonal distance to the top of the street light, is 16 feet, and she is standing 8 feet from the base of the street light. Use the inverse of cosine to find the angle of elevation with which she is looking at the bird. Round your answer to the nearest whole degree. (1 point) °

Answer 1

To find the angle of elevation from Meekah to the bird perched on top of the street light, we can use the cosine function and its inverse.

We have:

• The adjacent side (the distance from Meekah to the base of the street light) is 8 feet.
• The hypotenuse (the line of sight to the bird) is 16 feet.

We can use the cosine function, which is defined as:

\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]

Substituting in the known values:

\[ \cos(\theta) = \frac{8}{16} = 0.5 \]

To find the angle \(\theta\), we take the inverse cosine:

\[ \theta = \cos^{-1}(0.5) \]

From trigonometry, we know that:

\[ \theta = 60^\circ \]

So, the angle of elevation with which Meekah is looking at the bird is:

\[ \boxed{60} \text{ degrees} \]