Question

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A stake is to be driven into the ground 38 feet from the base of a pole, as shown in the diagram below. A wire from the stake on the ground to the top of the pole is to be installed at an angle of elevation of 52º. What will be the length of the wire from the stake to the top of the pole, to the nearest hundredth of a foot.

Answer 1

you have to do 52 divided by cos of 38 to get the answer of 65.99ft

Answer 2

The length of the wire from the stake to the top of the pole, with a 52-degree angle of elevation, is approximately 48.76 feet, rounded to the nearest hundredth.

To find the length of the wire, you can use trigonometry. The situation forms a right-angled triangle with the pole, the ground, and the wire as its sides. The angle of elevation (angle θ) is 52 degrees, and the horizontal distance from the stake to the base of the pole is 38 feet.

Using the tangent function:

`\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]`

In this case, opposite is the height of the pole, and adjacent is the horizontal distance (38 feet). So:

`\[ \tan(52^\circ) = \frac{\text{height}}{38} \]`

Now, solve for the height (length of the wire):

`\[ \text{height} = 38 * \tan(52^\circ) \]\[ \text{height} \approx 38 * 1.27994 \]\[ \text{height} \approx 48.75722 \]`

Therefore, the length of the wire from the stake to the top of the pole is approximately 48.76 feet (rounded to the nearest hundredth).