Clark Kent and Lois Lane were laying on a blanket, enjoying a relaxing picnic when Clark noticed a giant asteroid approaching Ea
rth. Clark calculates the angle of elevation of the asteroid's approach to be 62°. Lois' penthouse apartment is also in the pathway of the asteroid's approach, 100 feet above ground. Clark's eye is 75 feet from the base of Lois' building. Will the asteroid take out Lois' penthouse apartment?
Since the distance between Clark and the base of Lois' building is x = 75 feet and the asteroid is at an angle of elevation of Ф = 62°. These two components form a right-angled triangle with opposite side h which is the height of the asteroid above the ground.
So, by trigonometric ratios,
tanФ = h/x
h = xtanФ
h = 75 ft × tan62°
h = 75 ft × 1.8807
h = 141.1 feet
Since h = height of asteroid above the ground = 141.1 feet is greater than height of the penthouse above the ground = 100 feet, the asteroid will not take out Lois' penthouse.
