Answer :
The time at which the drone's altitude reach 500 feet is given by the equation T = 15 minutes
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the drone's height at 500 feet be represented as T
Now , the equation for drone's height is given by
h ( t ) = 450 + 50 [ sin ( t - 5 ) π/20 ] be equation (1)
where , h ( t ) is the height of drone
when height of the drone is at 500 feet
Substituting the value of h ( t ) = 500 in the equation , we get
500 = 450 + 50 [ sin ( t - 5 ) π/20 ]
On simplifying the equation , we get
Subtracting 450 on both sides of the equation , we get
50 = 50 [ sin ( t - 5 ) π/20 ]
Divide by 50 on both sides of the equation , we get
sin ( t - 5 ) π/20 = 1
From the trigonometric relations , sin 90° = 1
So , sin ( π/2 ) = 1
Substituting the values in the equation , we get
sin ( π/2 ) = sin ( t - 5 ) π/20
On further simplification , we get
( π/2 ) = ( t - 5 ) π/20
Multiply by 20 on both sides of the equation , we get
( t - 5 ) = 10
Adding 5 on both sides , we get
t = 15 minutes
Hence , the time required is 15 minutes to reach 500 feet
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