QuestionFind the distance from the base of the left field wall to the point below the seats, given height 90 ft and angle $14^{\circ}$ .

Studdy Solution

STEP 1

Assumptions1. The top row of the red seats behind home plate at Cincinnati's Riverfront stadium is90 ft above the level of the playing field. . The angle of depression of the base of the left field wall is $14^{\circ}$ .
3. We are looking for the distance from a point on the ground directly below the top row to the base of the left field wall.
4. We assume the ground is level and the wall is perpendicular to the ground, forming a right triangle.

STEP 2

We will use the tangent of the angle of depression to find the distance from the point directly below the top row to the base of the left field wall. 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 our case, the opposite side is the height of the top row above the playing field (90 ft), and the adjacent side is the distance we are trying to find. So we can rewrite the equation as $tan(14^{\circ}) = \frac{90}{distance}$

STEP 4

We can solve for the distance by rearranging the equation $distance = \frac{90}{tan(14^{\circ})}$

STEP 5

Now we can plug in the value for the tangent of $14^{\circ}$ and calculate the distance.
$distance = \frac{90}{tan(14^{\circ})}$

STEP 6

The tangent of $14^{\circ}$ is approximately0.2493 (using a calculator or a trigonometric table).
$distance = \frac{90}{0.2493}$

STEP 7

Calculate the distance.
$distance = \frac{90}{0.2493} \approx361.02 \, ft$ The base of the left field wall is approximately361.02 ft from a point on the ground directly below the top row.

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QuestionFind the distance from the base of the left field wall to the point below the seats, given height 90 ft and angle $14^{\circ}$ .

Studdy Solution

STEP 1

STEP 2

STEP 3

In our case, the opposite side is the height of the top row above the playing field (90 ft), and the adjacent side is the distance we are trying to find. So we can rewrite the equation as $tan(14^{\circ}) = \frac{90}{distance}$

STEP 4

We can solve for the distance by rearranging the equation $distance = \frac{90}{tan(14^{\circ})}$

STEP 5

Now we can plug in the value for the tangent of $14^{\circ}$ and calculate the distance.
$distance = \frac{90}{tan(14^{\circ})}$

STEP 6

The tangent of $14^{\circ}$ is approximately0.2493 (using a calculator or a trigonometric table).
$distance = \frac{90}{0.2493}$

STEP 7

Calculate the distance.
$distance = \frac{90}{0.2493} \approx361.02 \, ft$ The base of the left field wall is approximately361.02 ft from a point on the ground directly below the top row.

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QuestionFind the distance from the base of the left field wall to the point below the seats, given height 90 ft and angle 14∘14^{\circ}14∘.

Studdy Solution

STEP 1

STEP 2

STEP 3

In our case, the opposite side is the height of the top row above the playing field (90 ft), and the adjacent side is the distance we are trying to find. So we can rewrite the equation astan(14∘)=90distancetan(14^{\circ}) = \frac{90}{distance}tan(14∘)=distance90​

STEP 4

We can solve for the distance by rearranging the equationdistance=90tan(14∘)distance = \frac{90}{tan(14^{\circ})}distance=tan(14∘)90​

STEP 5

Now we can plug in the value for the tangent of 14∘14^{\circ}14∘ and calculate the distance.distance=90tan(14∘)distance = \frac{90}{tan(14^{\circ})}distance=tan(14∘)90​

STEP 6

The tangent of 14∘14^{\circ}14∘ is approximately0.2493 (using a calculator or a trigonometric table).distance=900.2493distance = \frac{90}{0.2493}distance=0.249390​

STEP 7

Calculate the distance.distance=900.2493≈361.02 ftdistance = \frac{90}{0.2493} \approx361.02 \, ftdistance=0.249390​≈361.02ftThe base of the left field wall is approximately361.02 ft from a point on the ground directly below the top row.

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

QuestionFind the distance from the base of the left field wall to the point below the seats, given height 90 ft and angle $14^{\circ}$ .

In our case, the opposite side is the height of the top row above the playing field (90 ft), and the adjacent side is the distance we are trying to find. So we can rewrite the equation as $tan(14^{\circ}) = \frac{90}{distance}$

We can solve for the distance by rearranging the equation $distance = \frac{90}{tan(14^{\circ})}$

Now we can plug in the value for the tangent of $14^{\circ}$ and calculate the distance.
$distance = \frac{90}{tan(14^{\circ})}$

The tangent of $14^{\circ}$ is approximately0.2493 (using a calculator or a trigonometric table).
$distance = \frac{90}{0.2493}$

Calculate the distance.
$distance = \frac{90}{0.2493} \approx361.02 \, ft$ The base of the left field wall is approximately361.02 ft from a point on the ground directly below the top row.