Question is:
During a windstorm, part of the top of a flagpole breaks off. The broken top portion touches the ground at an angle of 75 deg 19 feet from its base.
How tall was the pole before the windstorm?
I am having a hard time figuring out how exactly the sketch would be set up for me to start to solve the problem.
The broken part will form the hypotenuse of a right triangle...call this x
And we know an angle and an adjacent side [19] to this angle.....
So.....the trig relationship that best describes this is the cosine.....so
cos 75 = 19 / x rearrange
x = 19 / cos 75 = about 73.41 ft
And the height of the standing part, h, can be found by the tangent.....so we have
tan 75 = h / 19
h = 19 * tan 75 = about 70.91 ft
The total height of the pole is the sum of these = 73.41 + 70.91 = about 144.32 ft
During a windstorm, part of the top of a flagpole breaks off. The broken top portion touches the ground at an angle of 75 deg 19 feet from its base.
Tan(75)=Height of broken pole/19
3.732=H/19
H=19 X 3.732
H=70.908 feet-Length of the pole before windstorm.
Solving for "a" only gives the broken flag pole length, so what would I do next to find the length of the broken portion?
Because you have tow sides, use Pythagoras's Theorem:
Broken part=Hypotenuse
H^2=19^2 + 70.908^2
H^2=5,388.94 take the sqrt of both sides
H=73.41 feet-Length of the broken portion.
The broken part will form the hypotenuse of a right triangle...call this x
And we know an angle and an adjacent side [19] to this angle.....
So.....the trig relationship that best describes this is the cosine.....so
cos 75 = 19 / x rearrange
x = 19 / cos 75 = about 73.41 ft
And the height of the standing part, h, can be found by the tangent.....so we have
tan 75 = h / 19
h = 19 * tan 75 = about 70.91 ft
The total height of the pole is the sum of these = 73.41 + 70.91 = about 144.32 ft