QuestionCalculate the height of the kite above the ground if the handle is $80 \mathrm{~cm}$ high and the string is $8 \mathrm{~m}$ at $63^{\circ}$ .

Studdy Solution

STEP 1

Assumptions1. The handle is held80 cm above the ground. . The string is8 m long.
3. The string makes an angle of63 degrees with the horizontal.
4. We are asked to find the height of the bottom of the kite above the ground.
5. We are assuming that the string is taut and straight.

STEP 2

First, we need to convert the length of the string from meters to centimeters because the height of the handle is given in centimeters and we need to keep the units consistent.
$Length\, of\, string =8\, m =800\, cm$

STEP 3

We can use the trigonometric function sine to calculate the height of the kite from the handle. The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
$Height\, from\, handle = Length\, of\, string \\times \sin(Angle)$

STEP 4

Now, plug in the given values for the length of the string and the angle to calculate the height from the handle.
$Height\, from\, handle =800\, cm \\times \sin(63^{\circ})$

STEP 5

Calculate the height of the kite from the handle.
$Height\, from\, handle \approx800\, cm \\times0.891 =712.8\, cm$

STEP 6

Now that we have the height of the kite from the handle, we can find the total height of the kite above the ground by adding the height of the handle.
$Total\, height = Height\, from\, handle + Height\, of\, handle$

STEP 7

Plug in the values for the height from the handle and the height of the handle to calculate the total height.
$Total\, height =712.\, cm +80\, cm$

STEP 8

Calculate the total height of the kite above the ground.
$Total\, height =712.8\, cm +80\, cm =792.8\, cm$ The bottom of the kite is approximately792.8 cm above the ground.

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