Math / Trigonometry

QuestionShow 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 1 out of 2 $\square$ Submit Answer

Studdy Solution

STEP 1

1. The tree is vertical, and the ground is level.
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.

STEP 2

1. Understand the trigonometric relationship.
2. Set up the equation using the tangent function.
3. Solve for the angle of elevation.
4. Round the answer to the nearest tenth of a degree.

STEP 3

Understand the trigonometric relationship:
The angle of elevation can be found using the tangent function, which relates the opposite side (height of the tree) to the adjacent side (distance from the tree).

STEP 4

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

STEP 5

Solve for the angle of elevation:
Use the inverse tangent function to find $\theta$ :
$\theta = \tan^{-1}\left(\frac{126}{79}\right)$
Calculate $\theta$ using a calculator:
$\theta \approx \tan^{-1}(1.5949)$
$\theta \approx 57.4^\circ$

STEP 6

Round the answer to the nearest tenth of a degree:
The angle of elevation is approximately:
$\boxed{57.4^\circ}$

Was this helpful?

QuestionShow 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 1 out of 2 $\square$ Submit Answer

Studdy Solution

STEP 1

1. The tree is vertical, and the ground is level.
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.

STEP 2

1. Understand the trigonometric relationship.
2. Set up the equation using the tangent function.
3. Solve for the angle of elevation.
4. Round the answer to the nearest tenth of a degree.

STEP 3

Understand the trigonometric relationship:
The angle of elevation can be found using the tangent function, which relates the opposite side (height of the tree) to the adjacent side (distance from the tree).

STEP 4

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

STEP 5

Solve for the angle of elevation:
Use the inverse tangent function to find $\theta$ :
$\theta = \tan^{-1}\left(\frac{126}{79}\right)$
Calculate $\theta$ using a calculator:
$\theta \approx \tan^{-1}(1.5949)$
$\theta \approx 57.4^\circ$

STEP 6

Round the answer to the nearest tenth of a degree:
The angle of elevation is approximately:
$\boxed{57.4^\circ}$

Get Studdy

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.

QuestionShow 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 1 out of 2 □\square□ Submit Answer

Studdy Solution

STEP 1

1. The tree is vertical, and the ground is level.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.

STEP 2

1. Understand the trigonometric relationship.2. Set up the equation using the tangent function.3. Solve for the angle of elevation.4. Round the answer to the nearest tenth of a degree.

STEP 3

Understand the trigonometric relationship:The angle of elevation can be found using the tangent function, which relates the opposite side (height of the tree) to the adjacent side (distance from the tree).

STEP 4

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

STEP 5

STEP 6

Round the answer to the nearest tenth of a degree:The angle of elevation is approximately:57.4∘ \boxed{57.4^\circ} 57.4∘​

Get Studdy

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.

QuestionShow 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 1 out of 2 $\square$ Submit Answer

1. The tree is vertical, and the ground is level.
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.

1. Understand the trigonometric relationship.
2. Set up the equation using the tangent function.
3. Solve for the angle of elevation.
4. Round the answer to the nearest tenth of a degree.

Understand the trigonometric relationship:
The angle of elevation can be found using the tangent function, which relates the opposite side (height of the tree) to the adjacent side (distance from the tree).

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

Round the answer to the nearest tenth of a degree:
The angle of elevation is approximately:
$\boxed{57.4^\circ}$