Final answer:
The height of the blimp can be determined by setting up a triangle with the football field and using the law of sines with the known angles of elevation and the distance between the end zones. By finding the third angle of the triangle and using the law of sines, we obtain lengths from directly below the blimp to the end zones, allowing us to calculate the height using basic trigonometry.
Step-by-step explanation:
To find the height of the blimp from the ground using the law of sines, we first need to set up a triangle with the two angles of elevation and the distance between the end zones of the football field. Let the distance from the ground directly beneath the blimp to one end zone be a and to the other end zone be b. The length of the football field, which is the side opposite the blimp, is c = 120 yards. The angles of elevation to the blimp from the end zones are α = 70° and β = 62°. Using the law of sines, we have:
α / sin(γ) = a / sin(β) = b / sin(α)
Let's find the third angle of the triangle using the fact that the sum of angles in a triangle is 180 degrees: γ = 180° - α - β = 180° - 70° - 62° = 48°.
We can then solve for a and b using the law of sines. Once we have a and b, we can use basic trigonometry to find the height h of the blimp:
h = a * sin(β) = b * sin(α)
Through calculations, we would obtain values for a and b and thereby find the height of the blimp from the ground.