The angle of elevation from the ground is 68 degrees. Franklin has used 1,890 feet of string. What is the approximate height of the kite? Round to the nearest whole number and make sure to show ALL of your work!

Answer 1

To find the height of the kite based on the given angle of elevation and the length of string used, we'll use trigonometry.

We have:

• θ (angle of elevation) = 68 degrees
• L (length of the string) = 1,890 feet

We can visualize this problem as a right triangle where:

• The string acts as the hypotenuse (L).
• The height of the kite is the opposite side to the angle of elevation.
• The ground (horizontal distance) is the adjacent side.

Using the sine function: \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] In this case: \[ \sin(68^\circ) = \frac{\text{height}}{1890} \]

To find the height, we rearrange the formula: \[ \text{height} = L \cdot \sin(\theta) \]

Now, plug in the values: \[ \text{height} = 1890 \cdot \sin(68^\circ) \]

Next, we'll calculate \( \sin(68^\circ) \). Using a calculator, we find: \[ \sin(68^\circ) \approx 0.92718 \]

Now calculate the height: \[ \text{height} \approx 1890 \cdot 0.92718 \approx 1753.6192 \]

Rounding to the nearest whole number: \[ \text{height} \approx 1754 \text{ feet} \]

Thus, the approximate height of the kite is 1754 feet.

Answer 2

Make a summary

Answer 3

To determine the height of a kite based on an angle of elevation of 68 degrees and a string length of 1,890 feet, we used trigonometric functions. By applying the sine function:

\[ \sin(68^\circ) = \frac{\text{height}}{1890} \]

we rearranged the formula to calculate the height:

\[ \text{height} = 1890 \cdot \sin(68^\circ) \]

Using a calculator, we found \( \sin(68^\circ) \approx 0.92718 \). Therefore:

\[ \text{height} \approx 1890 \cdot 0.92718 \approx 1753.62 \]

After rounding to the nearest whole number, the approximate height of the kite is 1754 feet.