Math / Trigonometry

Questiontower?
61. Elevation of a Kite A tourist is lying on the beach, flying a kite. The tourist holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be $50^{\circ}$ . If the string is 450 ft long, how high is the kite above the ground?

Studdy Solution

STEP 1

1. The kite string forms a straight line from the tourist to the kite.
2. The angle of elevation is measured from the horizontal ground to the kite string.
3. The length of the kite string is $450$ feet.
4. The angle of elevation is $50^\circ$ .

STEP 2

1. Identify the right triangle formed by the kite string, the height of the kite, and the horizontal distance.
2. Recall the trigonometric relationship for the angle of elevation.
3. Substitute the given values into the trigonometric equation.
4. Solve for the height of the kite.

STEP 3

Identify the right triangle formed by the kite string. The hypotenuse is the kite string, the opposite side is the height of the kite, and the adjacent side is the horizontal distance from the tourist to the point directly below the kite.

STEP 4

Recall the trigonometric relationship for the angle of elevation, which involves the sine function:
$\sin(\theta) = \frac{\text{Opposite Side}}{\text{Hypotenuse}}$
In this context, the opposite side is the height of the kite, and the hypotenuse is the length of the kite string.

STEP 5

Substitute the given values into the trigonometric equation:
$\sin(50^\circ) = \frac{h}{450}$
where $h$ is the height of the kite.

STEP 6

Solve for the height $h$ :
$h = 450 \times \sin(50^\circ)$
Calculate $\sin(50^\circ)$ using a calculator:
$\sin(50^\circ) \approx 0.7660$
Now, calculate $h$ :
$h = 450 \times 0.7660$ $h \approx 344.7$
The height of the kite above the ground is approximately:
$\boxed{344.7 \text{ ft}}$

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Questiontower?
61. Elevation of a Kite A tourist is lying on the beach, flying a kite. The tourist holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be $50^{\circ}$ . If the string is 450 ft long, how high is the kite above the ground?

Studdy Solution

STEP 1

1. The kite string forms a straight line from the tourist to the kite.
2. The angle of elevation is measured from the horizontal ground to the kite string.
3. The length of the kite string is $450$ feet.
4. The angle of elevation is $50^\circ$ .

STEP 2

1. Identify the right triangle formed by the kite string, the height of the kite, and the horizontal distance.
2. Recall the trigonometric relationship for the angle of elevation.
3. Substitute the given values into the trigonometric equation.
4. Solve for the height of the kite.

STEP 3

Identify the right triangle formed by the kite string. The hypotenuse is the kite string, the opposite side is the height of the kite, and the adjacent side is the horizontal distance from the tourist to the point directly below the kite.

STEP 4

Recall the trigonometric relationship for the angle of elevation, which involves the sine function:
$\sin(\theta) = \frac{\text{Opposite Side}}{\text{Hypotenuse}}$
In this context, the opposite side is the height of the kite, and the hypotenuse is the length of the kite string.

STEP 5

Substitute the given values into the trigonometric equation:
$\sin(50^\circ) = \frac{h}{450}$
where $h$ is the height of the kite.

STEP 6

Solve for the height $h$ :
$h = 450 \times \sin(50^\circ)$
Calculate $\sin(50^\circ)$ using a calculator:
$\sin(50^\circ) \approx 0.7660$
Now, calculate $h$ :
$h = 450 \times 0.7660$ $h \approx 344.7$
The height of the kite above the ground is approximately:
$\boxed{344.7 \text{ ft}}$

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Questiontower?61. Elevation of a Kite A tourist is lying on the beach, flying a kite. The tourist holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be 50∘50^{\circ}50∘. If the string is 450 ft long, how high is the kite above the ground?

Studdy Solution

STEP 1

1. The kite string forms a straight line from the tourist to the kite.2. The angle of elevation is measured from the horizontal ground to the kite string.3. The length of the kite string is 450 450 450 feet.4. The angle of elevation is 50∘ 50^\circ 50∘.

STEP 2

1. Identify the right triangle formed by the kite string, the height of the kite, and the horizontal distance.2. Recall the trigonometric relationship for the angle of elevation.3. Substitute the given values into the trigonometric equation.4. Solve for the height of the kite.

STEP 3

Identify the right triangle formed by the kite string. The hypotenuse is the kite string, the opposite side is the height of the kite, and the adjacent side is the horizontal distance from the tourist to the point directly below the kite.

STEP 4

STEP 5

Substitute the given values into the trigonometric equation:sin⁡(50∘)=h450 \sin(50^\circ) = \frac{h}{450} sin(50∘)=450h​where h h h is the height of the kite.

STEP 6

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Questiontower?
61. Elevation of a Kite A tourist is lying on the beach, flying a kite. The tourist holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be $50^{\circ}$ . If the string is 450 ft long, how high is the kite above the ground?

1. The kite string forms a straight line from the tourist to the kite.
2. The angle of elevation is measured from the horizontal ground to the kite string.
3. The length of the kite string is $450$ feet.
4. The angle of elevation is $50^\circ$ .

1. Identify the right triangle formed by the kite string, the height of the kite, and the horizontal distance.
2. Recall the trigonometric relationship for the angle of elevation.
3. Substitute the given values into the trigonometric equation.
4. Solve for the height of the kite.

Substitute the given values into the trigonometric equation:
$\sin(50^\circ) = \frac{h}{450}$
where $h$ is the height of the kite.