Solved on Jan 28, 2024

Find the height of a pole using a 38-foot wire attached at a 14-degree angle to the ground. Round the height to the nearest tenth of a foot.
$\tan(14^\circ) = \frac{\text{pole height}}{38}$

STEP 1

Assumptions
1. The length of the wire is 38 feet.
2. The wire makes a 14 degree angle with the ground.
3. The wire is attached to the top of the pole and anchored to the ground, forming a right triangle with the pole and the ground.
4. We are to use trigonometric functions to solve the problem.
5. The answer should be rounded to the nearest tenth of a foot.

STEP 2

Identify the trigonometric function that relates the angle, the length of the wire, and the height of the pole. Since we have the angle the wire makes with the ground and we want to find the height (opposite side) of the pole, we will use the sine function.
$\sin(\theta) = \frac{opposite}{hypotenuse}$

STEP 3

Plug in the given values for the angle and the length of the wire (hypotenuse) into the sine function.
$\sin(14^\circ) = \frac{height\,of\,the\,pole}{38\,feet}$

STEP 4

Solve for the height of the pole by multiplying both sides by the length of the wire.
$height\,of\,the\,pole = \sin(14^\circ) \times 38\,feet$

STEP 5

Use a calculator to find the sine of 14 degrees. Make sure the calculator is in degree mode.
$\sin(14^\circ) \approx 0.24192$

STEP 6

Now calculate the height of the pole.
$height\,of\,the\,pole = 0.24192 \times 38\,feet$

STEP 7

Perform the multiplication to find the height of the pole.
$height\,of\,the\,pole \approx 0.24192 \times 38 \approx 9.19296$

STEP 8

Round the height of the pole to the nearest tenth of a foot.
$height\,of\,the\,pole \approx 9.2$
The height of the pole is approximately 9.2 feet.

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Find the height of a pole using a 38-foot wire attached at a 14-degree angle to the ground. Round the height to the nearest tenth of a foot.
$\tan(14^\circ) = \frac{\text{pole height}}{38}$

STEP 1

STEP 2

STEP 3

Plug in the given values for the angle and the length of the wire (hypotenuse) into the sine function.
$\sin(14^\circ) = \frac{height\,of\,the\,pole}{38\,feet}$

STEP 4

Solve for the height of the pole by multiplying both sides by the length of the wire.
$height\,of\,the\,pole = \sin(14^\circ) \times 38\,feet$

STEP 5

Use a calculator to find the sine of 14 degrees. Make sure the calculator is in degree mode.
$\sin(14^\circ) \approx 0.24192$

STEP 6

Now calculate the height of the pole.
$height\,of\,the\,pole = 0.24192 \times 38\,feet$

STEP 7

Perform the multiplication to find the height of the pole.
$height\,of\,the\,pole \approx 0.24192 \times 38 \approx 9.19296$

STEP 8

Round the height of the pole to the nearest tenth of a foot.
$height\,of\,the\,pole \approx 9.2$
The height of the pole is approximately 9.2 feet.

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Find the height of a pole using a 38-foot wire attached at a 14-degree angle to the ground. Round the height to the nearest tenth of a foot.tan⁡(14∘)=pole height38\tan(14^\circ) = \frac{\text{pole height}}{38}tan(14∘)=38pole height​

STEP 1

STEP 2

STEP 3

Plug in the given values for the angle and the length of the wire (hypotenuse) into the sine function.sin⁡(14∘)=height of the pole38 feet\sin(14^\circ) = \frac{height\,of\,the\,pole}{38\,feet}sin(14∘)=38feetheightofthepole​

STEP 4

Solve for the height of the pole by multiplying both sides by the length of the wire.height of the pole=sin⁡(14∘)×38 feetheight\,of\,the\,pole = \sin(14^\circ) \times 38\,feetheightofthepole=sin(14∘)×38feet

STEP 5

Use a calculator to find the sine of 14 degrees. Make sure the calculator is in degree mode.sin⁡(14∘)≈0.24192\sin(14^\circ) \approx 0.24192sin(14∘)≈0.24192

STEP 6

Now calculate the height of the pole.height of the pole=0.24192×38 feetheight\,of\,the\,pole = 0.24192 \times 38\,feetheightofthepole=0.24192×38feet

STEP 7

Perform the multiplication to find the height of the pole.height of the pole≈0.24192×38≈9.19296height\,of\,the\,pole \approx 0.24192 \times 38 \approx 9.19296heightofthepole≈0.24192×38≈9.19296

STEP 8

Round the height of the pole to the nearest tenth of a foot.height of the pole≈9.2height\,of\,the\,pole \approx 9.2heightofthepole≈9.2The height of the pole is approximately 9.2 feet.

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

Find the height of a pole using a 38-foot wire attached at a 14-degree angle to the ground. Round the height to the nearest tenth of a foot.
$\tan(14^\circ) = \frac{\text{pole height}}{38}$

Plug in the given values for the angle and the length of the wire (hypotenuse) into the sine function.
$\sin(14^\circ) = \frac{height\,of\,the\,pole}{38\,feet}$

Solve for the height of the pole by multiplying both sides by the length of the wire.
$height\,of\,the\,pole = \sin(14^\circ) \times 38\,feet$

Use a calculator to find the sine of 14 degrees. Make sure the calculator is in degree mode.
$\sin(14^\circ) \approx 0.24192$

Now calculate the height of the pole.
$height\,of\,the\,pole = 0.24192 \times 38\,feet$

Perform the multiplication to find the height of the pole.
$height\,of\,the\,pole \approx 0.24192 \times 38 \approx 9.19296$

Round the height of the pole to the nearest tenth of a foot.
$height\,of\,the\,pole \approx 9.2$
The height of the pole is approximately 9.2 feet.