During a windstorm, part of the top of a flagpole breaks off. The broken top portion touches the ground at an angle of 65 degrees, 14 feet from its base.
How tall was the pole before the windstorm? Round your answer to one decimal place.
Answer (2)
The situation in the problem creates a right triangle with a base of 14ft. An angle of 65 degrees means that the triangles has...
A hypotenuse of h y p = cos ( 45 ) 14 f t = 33.13 f t , representing the length of the broken part of the pole.
An opposite of s in ( 65 ) ∗ h y p = s in ( 65 ) ∗ 33.1 f t = 30.0 f t , representing the height of the part of the flag that still stands.
The total original flag height is the sum of the two parts. h = 30.0 f t + 33.13 f t = 63.13 f t
The original height of the flagpole before the windstorm was approximately 63.1 feet after using trigonometry to determine the lengths of the standing and broken parts. This was calculated using the cosine and sine functions based on the right triangle formed by the angle and distance from the base. Therefore, the flagpole was around 63.1 feet tall.
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