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. She is standing 8 feet from the base of the street light. What is the angle of elevation with which she is looking at the bird. Round your answer to the nearest whole degree.

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. She is standing 8 feet from the base of the street light. What is the angle of elevation with which she is looking at the bird. Round your answer to the nearest whole degree.

Answer 1

We have a right triangle formed by Meekah, the bird, and the base of the street light. The diagonal distance to the top of the street light forms the hypotenuse of the triangle. The base of the triangle is the distance Meekah is standing from the base of the street light. So, we have a right triangle with a hypotenuse of 16 ft and a base of 8 ft.

To find the angle of elevation, we can use the inverse tangent function (arctan) to find the angle whose tangent is the ratio of the length of the side opposite the angle (8 ft) to the length of the side adjacent to the angle (16 ft).

Using the formula: angle = arctan(opposite/adjacent)

angle = arctan(8/16) = arctan(0.5)

Using a calculator, we find that arctan(0.5) is approximately 26.57 degrees.

Rounded to the nearest whole degree, the angle of elevation is 27 degrees.