QuestionFind the distance to the base of a plateau 19.6 m high with an elevation angle of $16.5^{\circ}$ . Round to one decimal place.

Studdy Solution

STEP 1

Assumptions1. The height of the plateau is19.6 meters. The angle of elevation to the top of the plateau is $16.5^{\circ}$
3. We are looking for the distance from the base of the plateau4. We assume the situation forms a right triangle, with the plateau as one side, the distance we want to find as the other side, and the line of sight to the top of the plateau as the hypotenuse.

STEP 2

We can use the tangent of the angle of elevation to find the distance from the base of the plateau. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side.
$\tan(\theta) = \frac{opposite}{adjacent}$

STEP 3

In this case, the opposite side is the height of the plateau and the adjacent side is the distance from the base of the plateau, which we are trying to find.
$\tan(16.5^{\circ}) = \frac{19.6}{distance}$

STEP 4

To find the distance, we rearrange the equation to solve for distance.
$distance = \frac{19.6}{\tan(16.^{\circ})}$

STEP 5

Now, we can plug in the values and calculate the distance.
$distance = \frac{19.}{\tan(16.5^{\circ})}$

STEP 6

Calculate the distance from the base of the plateau.
$distance = \frac{19.6}{\tan(16.5^{\circ})} =67.8 \, meters$ You are approximately67.8 meters from the base of the plateau.

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QuestionFind the distance to the base of a plateau 19.6 m high with an elevation angle of $16.5^{\circ}$ . Round to one decimal place.

Studdy Solution

STEP 1

STEP 2

We can use the tangent of the angle of elevation to find the distance from the base of the plateau. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side.
$\tan(\theta) = \frac{opposite}{adjacent}$

STEP 3

In this case, the opposite side is the height of the plateau and the adjacent side is the distance from the base of the plateau, which we are trying to find.
$\tan(16.5^{\circ}) = \frac{19.6}{distance}$

STEP 4

To find the distance, we rearrange the equation to solve for distance.
$distance = \frac{19.6}{\tan(16.^{\circ})}$

STEP 5

Now, we can plug in the values and calculate the distance.
$distance = \frac{19.}{\tan(16.5^{\circ})}$

STEP 6

Calculate the distance from the base of the plateau.
$distance = \frac{19.6}{\tan(16.5^{\circ})} =67.8 \, meters$ You are approximately67.8 meters from the base of the plateau.

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QuestionFind the distance to the base of a plateau 19.6 m high with an elevation angle of 16.5∘16.5^{\circ}16.5∘. Round to one decimal place.

Studdy Solution

STEP 1

STEP 2

STEP 3

In this case, the opposite side is the height of the plateau and the adjacent side is the distance from the base of the plateau, which we are trying to find.tan⁡(16.5∘)=19.6distance\tan(16.5^{\circ}) = \frac{19.6}{distance}tan(16.5∘)=distance19.6​

STEP 4

To find the distance, we rearrange the equation to solve for distance.distance=19.6tan⁡(16.∘)distance = \frac{19.6}{\tan(16.^{\circ})}distance=tan(16.∘)19.6​

STEP 5

Now, we can plug in the values and calculate the distance.distance=19.tan⁡(16.5∘)distance = \frac{19.}{\tan(16.5^{\circ})}distance=tan(16.5∘)19.​

STEP 6

Calculate the distance from the base of the plateau.distance=19.6tan⁡(16.5∘)=67.8 metersdistance = \frac{19.6}{\tan(16.5^{\circ})} =67.8 \, metersdistance=tan(16.5∘)19.6​=67.8metersYou are approximately67.8 meters from the base of the plateau.

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QuestionFind the distance to the base of a plateau 19.6 m high with an elevation angle of $16.5^{\circ}$ . Round to one decimal place.

In this case, the opposite side is the height of the plateau and the adjacent side is the distance from the base of the plateau, which we are trying to find.
$\tan(16.5^{\circ}) = \frac{19.6}{distance}$

To find the distance, we rearrange the equation to solve for distance.
$distance = \frac{19.6}{\tan(16.^{\circ})}$

Now, we can plug in the values and calculate the distance.
$distance = \frac{19.}{\tan(16.5^{\circ})}$

Calculate the distance from the base of the plateau.
$distance = \frac{19.6}{\tan(16.5^{\circ})} =67.8 \, meters$ You are approximately67.8 meters from the base of the plateau.