"A kite is flying 100ft off the ground, and its line is pulled taut. The angle of elevation of the kite is 43 degrees. Find the length of the line."

To solve this problem, we can use the basic trigonometric function tangent (tan). The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

In this case, the opposite side is the height of the kite above the ground (100ft), and the adjacent side is the length of the line we are trying to find.

Let's use the formula for tangent:

tan(angle) = opposite/adjacent

Plugging in the given values, we have:

tan(43 degrees) = 100ft/adjacent

Now, we need to find the value of tangent(43 degrees). You can do this by using a calculator or by using a trigonometric table.

Assuming we find that tangent(43 degrees) is 0.932, we can rewrite our equation as:

0.932 = 100ft/adjacent

Next, we can solve for the adjacent side (length of the line) by multiplying both sides of the equation by the adjacent side:

0.932 * adjacent = 100ft

Dividing both sides of the equation by 0.932, we get:

adjacent ≈ 100ft / 0.932

This simplifies to:

adjacent ≈ 107.28 ft

So, the length of the line is approximately 107.28 ft.

To find the length of the line, we can use trigonometry.

Let's represent the length of the line as "x".

The angle of elevation of the kite tells us that the line forms a right triangle with the ground. The angle between the ground and the line is 90 degrees, and the angle between the line and the vertical (upward direction) is 43 degrees.

Using the trigonometric function tangent (tan), we can set up the following equation:

tan(43 degrees) = opposite/adjacent

The opposite side is the height at which the kite is flying, which is 100ft, and the adjacent side is the length of the line (x).

So, we have:

tan(43 degrees) = 100ft/x

To find x, we can rearrange the equation:

x = 100ft / tan(43 degrees)

Now, we can calculate the length of the line:

x = 100ft / tan(43 degrees)
x ≈ 100ft / 0.932
x ≈ 107.38ft

Therefore, the length of the line is approximately 107.38 feet.

sin 43 = 100/L