A person is standing 90 feet away from the Space Needle. The person looks up at the Space Needle at an angle of elevation of 81 degrees. The distance from the floor to the person's eye level is 5 feet. What must be the height of the Space Needle?
draw a diagram
review your basic trig functions.
(h-5)/90 = tan 81°
To find the height of the Space Needle, we can use trigonometry and the concept of similar triangles.
Let's define the following:
h = height of the Space Needle
d = distance from the floor to the person's eye level
θ = angle of elevation
From the given information, we know that:
Distance from the person to the Space Needle = 90 feet
Angle of elevation = 81 degrees
Distance from the floor to the person's eye level = 5 feet
Now, we can create a right-angled triangle with the following sides:
Adjacent side = Distance from the person to the Space Needle = 90 feet
Opposite side = Height of the Space Needle, which we need to find = h
Hypotenuse = Distance from the floor to the person's eye level + Height of the Space Needle = 5 + h
Using trigonometry, we can write the equation:
tan(θ) = Opposite/Adjacent
Plugging in the given values:
tan(81 degrees) = h/90
Now, we can solve this equation to find the height of the Space Needle, h.
1. Take the tangent of 81 degrees:
tan(81 degrees) ≈ 7.11537
2. Solve for h:
h/90 = 7.11537
Multiply both sides by 90:
h = 7.11537 * 90
Calculating the result:
h ≈ 639.3858
Therefore, the height of the Space Needle is approximately 639.3858 feet.