Math / Trigonometry

QuestionQuestion Show Examples
If a tree has a height of 126 feet, what would be the angle of elevation from level ground measured from 79 feet away? Round your answer to the nearest tenth of a degree.
Answer Attempt 2 out of 2 $\square$ 。 Submit Answer

Studdy Solution

STEP 1

1. The tree is standing vertically on level ground.
2. The distance from the point of observation to the base of the tree is $79$ feet.
3. The height of the tree is $126$ feet.
4. We are assuming a right triangle is formed with the tree height and the distance from the tree.

STEP 2

1. Identify the right triangle and the trigonometric function to use.
2. Set up the equation using the tangent function.
3. Solve for the angle of elevation.
4. Round the angle to the nearest tenth of a degree.

STEP 3

Identify the right triangle and the trigonometric function to use:
- The height of the tree is the opposite side of the angle. - The distance from the tree is the adjacent side. - Use the tangent function:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

STEP 4

Set up the equation using the tangent function:
$\tan(\theta) = \frac{126}{79}$

STEP 5

Solve for the angle of elevation $\theta$ :
$\theta = \tan^{-1}\left(\frac{126}{79}\right)$
Calculate $\theta$ using a calculator:
$\theta \approx \tan^{-1}(1.5949)$

STEP 6

Round the angle to the nearest tenth of a degree:
$\theta \approx 57.5^\circ$
The angle of elevation is:
$\boxed{57.5^\circ}$

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QuestionQuestion Show Examples
If a tree has a height of 126 feet, what would be the angle of elevation from level ground measured from 79 feet away? Round your answer to the nearest tenth of a degree.
Answer Attempt 2 out of 2 $\square$ 。 Submit Answer

Studdy Solution

STEP 1

1. The tree is standing vertically on level ground.
2. The distance from the point of observation to the base of the tree is $79$ feet.
3. The height of the tree is $126$ feet.
4. We are assuming a right triangle is formed with the tree height and the distance from the tree.

STEP 2

1. Identify the right triangle and the trigonometric function to use.
2. Set up the equation using the tangent function.
3. Solve for the angle of elevation.
4. Round the angle to the nearest tenth of a degree.

STEP 3

Identify the right triangle and the trigonometric function to use:
- The height of the tree is the opposite side of the angle. - The distance from the tree is the adjacent side. - Use the tangent function:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

STEP 4

Set up the equation using the tangent function:
$\tan(\theta) = \frac{126}{79}$

STEP 5

Solve for the angle of elevation $\theta$ :
$\theta = \tan^{-1}\left(\frac{126}{79}\right)$
Calculate $\theta$ using a calculator:
$\theta \approx \tan^{-1}(1.5949)$

STEP 6

Round the angle to the nearest tenth of a degree:
$\theta \approx 57.5^\circ$
The angle of elevation is:
$\boxed{57.5^\circ}$

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QuestionQuestion Show ExamplesIf a tree has a height of 126 feet, what would be the angle of elevation from level ground measured from 79 feet away? Round your answer to the nearest tenth of a degree.Answer Attempt 2 out of 2 □\square□。 Submit Answer

Studdy Solution

STEP 1

1. The tree is standing vertically on level ground.2. The distance from the point of observation to the base of the tree is 79 79 79 feet.3. The height of the tree is 126 126 126 feet.4. We are assuming a right triangle is formed with the tree height and the distance from the tree.

STEP 2

1. Identify the right triangle and the trigonometric function to use.2. Set up the equation using the tangent function.3. Solve for the angle of elevation.4. Round the angle to the nearest tenth of a degree.

STEP 3

STEP 4

Set up the equation using the tangent function:tan⁡(θ)=12679 \tan(\theta) = \frac{126}{79} tan(θ)=79126​

STEP 5

Solve for the angle of elevation θ\thetaθ:θ=tan⁡−1(12679) \theta = \tan^{-1}\left(\frac{126}{79}\right) θ=tan−1(79126​)Calculate θ\thetaθ using a calculator:θ≈tan⁡−1(1.5949) \theta \approx \tan^{-1}(1.5949) θ≈tan−1(1.5949)

STEP 6

Round the angle to the nearest tenth of a degree:θ≈57.5∘ \theta \approx 57.5^\circ θ≈57.5∘ The angle of elevation is:57.5∘ \boxed{57.5^\circ} 57.5∘​

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Studdy solves anything!

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

QuestionQuestion Show Examples
If a tree has a height of 126 feet, what would be the angle of elevation from level ground measured from 79 feet away? Round your answer to the nearest tenth of a degree.
Answer Attempt 2 out of 2 $\square$ 。 Submit Answer

1. The tree is standing vertically on level ground.
2. The distance from the point of observation to the base of the tree is $79$ feet.
3. The height of the tree is $126$ feet.
4. We are assuming a right triangle is formed with the tree height and the distance from the tree.

1. Identify the right triangle and the trigonometric function to use.
2. Set up the equation using the tangent function.
3. Solve for the angle of elevation.
4. Round the angle to the nearest tenth of a degree.

Set up the equation using the tangent function:
$\tan(\theta) = \frac{126}{79}$

Solve for the angle of elevation $\theta$ :
$\theta = \tan^{-1}\left(\frac{126}{79}\right)$
Calculate $\theta$ using a calculator:
$\theta \approx \tan^{-1}(1.5949)$

Round the angle to the nearest tenth of a degree:
$\theta \approx 57.5^\circ$
The angle of elevation is:
$\boxed{57.5^\circ}$