QuestionFind the angle of inclination of a $450-\mathrm{ft}$ ramp that rises $31-\mathrm{ft}$ to the nearest tenth of a degree.

Studdy Solution

STEP 1

Assumptions1. The ramp is450 ft long. . The ramp rises31 ft.
3. We are assuming the ramp forms a right triangle with the ground and the vertical rise.
4. We are asked to find the angle of inclination of the ramp to the nearest tenth of a degree.

STEP 2

The angle of inclination of the ramp can be found using the definition of tangent in a right triangle. The tangent of an angle in a right triangle is the ratio of the opposite side (rise) to the adjacent side (run). $\tan(\theta) = \frac{opposite}{adjacent}$

STEP 3

In this problem, the opposite side is the rise of the ramp, which is31 ft, and the adjacent side is the length of the ramp, which is450 ft. $\tan(\theta) = \frac{31}{450}$

STEP 4

To find the angle, we need to use the inverse tangent function (also called arctangent or atan), which gives the angle whose tangent is a given number.
$\theta = \arctan\left(\frac{31}{450}\right)$

STEP 5

Calculate the angle in radians.

STEP 6

Since we need the angle in degrees, we convert the result from radians to degrees using the conversion factor $\frac{180}{\pi}$ .
$\theta_{degrees} = \theta_{radians} \times \frac{180}{\pi}$

STEP 7

Calculate the angle in degrees.

STEP 8

Round the result to the nearest tenth of a degree.
The angle of inclination of the ramp to the nearest tenth of a degree is thus calculated.

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QuestionFind the angle of inclination of a $450-\mathrm{ft}$ ramp that rises $31-\mathrm{ft}$ to the nearest tenth of a degree.

Studdy Solution

STEP 1

Assumptions1. The ramp is450 ft long. . The ramp rises31 ft.
3. We are assuming the ramp forms a right triangle with the ground and the vertical rise.
4. We are asked to find the angle of inclination of the ramp to the nearest tenth of a degree.

STEP 2

The angle of inclination of the ramp can be found using the definition of tangent in a right triangle. The tangent of an angle in a right triangle is the ratio of the opposite side (rise) to the adjacent side (run). $\tan(\theta) = \frac{opposite}{adjacent}$

STEP 3

In this problem, the opposite side is the rise of the ramp, which is31 ft, and the adjacent side is the length of the ramp, which is450 ft. $\tan(\theta) = \frac{31}{450}$

STEP 4

To find the angle, we need to use the inverse tangent function (also called arctangent or atan), which gives the angle whose tangent is a given number.
$\theta = \arctan\left(\frac{31}{450}\right)$

STEP 5

Calculate the angle in radians.

STEP 6

Since we need the angle in degrees, we convert the result from radians to degrees using the conversion factor $\frac{180}{\pi}$ .
$\theta_{degrees} = \theta_{radians} \times \frac{180}{\pi}$

STEP 7

Calculate the angle in degrees.

STEP 8

Round the result to the nearest tenth of a degree.
The angle of inclination of the ramp to the nearest tenth of a degree is thus calculated.

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QuestionFind the angle of inclination of a 450−ft450-\mathrm{ft}450−ft ramp that rises 31−ft31-\mathrm{ft}31−ft to the nearest tenth of a degree.

Studdy Solution

STEP 1

Assumptions1. The ramp is450 ft long. . The ramp rises31 ft.3. We are assuming the ramp forms a right triangle with the ground and the vertical rise.4. We are asked to find the angle of inclination of the ramp to the nearest tenth of a degree.

STEP 2

STEP 3

In this problem, the opposite side is the rise of the ramp, which is31 ft, and the adjacent side is the length of the ramp, which is450 ft.tan⁡(θ)=31450\tan(\theta) = \frac{31}{450}tan(θ)=45031​

STEP 4

To find the angle, we need to use the inverse tangent function (also called arctangent or atan), which gives the angle whose tangent is a given number.θ=arctan⁡(31450)\theta = \arctan\left(\frac{31}{450}\right)θ=arctan(45031​)

STEP 5

Calculate the angle in radians.

STEP 6

Since we need the angle in degrees, we convert the result from radians to degrees using the conversion factor 180π\frac{180}{\pi}π180​.θdegrees=θradians×180π\theta_{degrees} = \theta_{radians} \times \frac{180}{\pi}θdegrees​=θradians​×π180​

STEP 7

Calculate the angle in degrees.

STEP 8

Round the result to the nearest tenth of a degree.The angle of inclination of the ramp to the nearest tenth of a degree is thus calculated.

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Studdy solves anything!

Start learning now

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

QuestionFind the angle of inclination of a $450-\mathrm{ft}$ ramp that rises $31-\mathrm{ft}$ to the nearest tenth of a degree.

Assumptions1. The ramp is450 ft long. . The ramp rises31 ft.
3. We are assuming the ramp forms a right triangle with the ground and the vertical rise.
4. We are asked to find the angle of inclination of the ramp to the nearest tenth of a degree.

In this problem, the opposite side is the rise of the ramp, which is31 ft, and the adjacent side is the length of the ramp, which is450 ft. $\tan(\theta) = \frac{31}{450}$

To find the angle, we need to use the inverse tangent function (also called arctangent or atan), which gives the angle whose tangent is a given number.
$\theta = \arctan\left(\frac{31}{450}\right)$

Since we need the angle in degrees, we convert the result from radians to degrees using the conversion factor $\frac{180}{\pi}$ .
$\theta_{degrees} = \theta_{radians} \times \frac{180}{\pi}$

Round the result to the nearest tenth of a degree.
The angle of inclination of the ramp to the nearest tenth of a degree is thus calculated.