A 50-foot wire running from the top of a tent pole to the ground makes an angle of 55° with the ground. If the length of the tent pole is 47 feet, how far is it from the bottom of the tent pole to the point where the wire is fastened to the ground? (The tent pole is not necessarily perpendicular to the ground.)Apply the rules regarding the use of significant digits after all computations are complete.
A)6 ft
B)3 ft
C)5.6 ft or 52 ft
D)52 ft
E)2.6 ft or 64 ft

Question

A 50-foot wire running from the top of a tent pole to the ground makes an angle of 55° with the ground. If the length of the tent pole is 47 feet, how far is it from the bottom of the tent pole to the point where the wire is fastened to the ground? (The tent pole is not necessarily perpendicular to the ground.)Apply the rules regarding the use of significant digits after all computations are complete. ​
A)6 ft
B)3 ft
C)5.6 ft or 52 ft
D)52 ft
E)2.6 ft or 64 ft

Quizplus · Accepted Answer

Using the trigonometric ratio tangent (tan):
tan(55°) = opposite/adjacent
where opposite = length of wire = 50 ft
and adjacent = distance from the bottom of the tent pole to the point where the wire is fastened to the ground (unknown)

Rearranging:
opposite/adjacent = tan(55°)
adjacent = opposite/tan(55°)
adjacent = 50/tan(55°)
adjacent ≈ 52 ft (rounded to two significant digits)

Since the length of the tent pole is given as 47 ft, we know that the distance from the bottom of the tent pole to the point where the wire is fastened to the ground is less than or equal to 47 ft. Therefore, the answer must be rounded to 2 significant digits, giving us 5.6 ft.

A 50-Foot Wire Running from the Top of a Tent