Raul is flying a kite at the end of a string that is 200 feet long. Raul is holding the string 5 feet off the ground at the angl
1 answer:
Answer:
Kite is 89.52 ft off the ground
Step-by-step explanation:
We are told that the string is 200 ft long.
That the string is 5 ft off the ground at an angle of 25° to the horizontal.
I have drawn a triangle to depict this illustration with x being the height of the kite from the end of the string.
Also, I have depicted the ground level which is 5 ft below the end of the string.
From the triangle, we can calculate the height of the kite above the end of the string using pythagoras theorem.
x/200 = sin 25
x = 200 sin 25
x = 200 × 0.4226
x = 84.52 ft
Now, the bottom of the kite is 5 ft off the ground as depicted in the attachment.
Thus, height of kite above the ground = 84.52 + 5 = 89.52 ft
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The hurdle and runner form a right triangle (see attached picture) such that
sin(30°) = <em>h</em> / (5 ft)
and
cos(30°) = <em>x</em> / (5 ft)
where <em>h</em> is the height of the hurdle and <em>x</em> is the horizontal distance from where the runner jumps to the hurdle. So
<em>h</em> = (5 ft) sin(30°) = 5/2 ft = 2.5 ft
<em>x</em> = (5 ft) cos(30°) = (5√3)/2 ft ≈ 4.33 ft
