A kite flying in the air has a
12ft line attached to it. Its line is pulled taut and casts an 11 ft shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth.
It seems to me where the SUN is matters. For a height remaining constant, the shadow gets longer as the day progresses.
If the Sun is directly overhead, then you have a right triangle:
h^2=12^2-11^2=144-121=23
height=sqrt23 ft That is not very high for kite flying, but 12 ft of line is hardly flying.
a^2 + b^2 = c^2
x^2 + 11^2 = 12^2
x^2 +121 =144
x^2 = 23
take the sq rt of 23 to find your answer.
16
To find the height of the kite, we can use similar triangles.
Let's denote the height of the kite as 'h' and the length of its shadow as 's'.
We can set up a proportion between the corresponding sides of the triangles:
(height of kite) / (length of shadow) = (length of the line) / (length of the line plus length of the shadow)
Using the given values, we have:
h / 11ft = 12ft / (12ft + 11ft)
Simplifying this equation, we get:
h / 11ft = 12ft / 23ft
Next, we can cross multiply:
h * 23ft = 12ft * 11ft
h * 23ft = 132ft²
Now, isolate 'h' by dividing both sides by 23ft:
h = 132ft² / 23ft
h ≈ 5.7391ft
Therefore, the height of the kite is approximately 5.7 ft.