Howard is flying a kite and wants to find its angle of elevation. The string on the kite is 32 meters long and the kite is level with the top of a building that he knows is 28 meters high.
To the nearest tenth of a degree, find the angle of elevation. Show your work.
To find the angle of elevation, we can use the trigonometric ratio of tangent. Tangent is defined as the opposite side divided by the adjacent side in a right triangle.
In this case, the opposite side is the height of the building (28 meters) and the adjacent side is the length of the string (32 meters).
So, let's calculate the tangent of the angle of elevation:
tan(angle of elevation) = opposite/adjacent
tan(angle of elevation) = 28/32
Now we can find the value of the angle of elevation by taking the inverse tangent of both sides:
angle of elevation = tan^(-1)(28/32)
Using a scientific calculator or trigonometric table, we can find the inverse tangent of 28/32 as:
angle of elevation ≈ 40.4 degrees
Therefore, to the nearest tenth of a degree, the angle of elevation is approximately 40.4 degrees.
To find the angle of elevation, we can use trigonometry. The angle of elevation is the angle between the horizontal line and the line from the observer (Howard) to the top of the building.
Let's call the angle of elevation θ, the length of the string L, and the height of the building H.
In this case, L = 32 meters and H = 28 meters.
We can use the tangent function to find the angle of elevation:
tan(θ) = H / L
Rearranging the equation, we have:
θ = arctan(H / L)
Substituting the given values, we have:
θ = arctan(28 / 32)
Now, using a scientific calculator or trigonometric tables, find the inverse tangent (arctan) of the ratio.
θ ≈ arctan(0.875) ≈ 40.67 degrees
Therefore, the angle of elevation is approximately 40.67 degrees.
Remember to round your answer to the nearest tenth of a degree, as requested.
According to my sketch,
sinØ = 28/32
Ø = ... I assume you have a calculator