Assuming that a 390390-foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be 49°49°, how far from the base of the tree am I? round to 4 decimal places

This problem involves solving for the distance from the base of the tree using trigonometry. Given the height of the tree (\( h = 390390 \, \text{ft} \)) and the angle of elevation (\( \theta = 49^\circ49' \)), we can apply the tangent function from trigonometry.

### Step-by-Step Solution:

The tangent of an angle in a right triangle is defined as:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

Where:
- The "opposite" side is the height of the tree (\( h = 390390 \, \text{ft} \)).
- The "adjacent" side is the distance from the base of the tree (\( d \)) that we need to find.

Rearranging the equation to solve for \( d \):

\[
d = \frac{h}{\tan(\theta)}
\]

Now, substitute the known values into the equation:

\[
d = \frac{390390}{\tan(49^\circ49')}
\]

I'll calculate the value of \( d \) for you.The distance from the base of the tree is approximately \( 329710.519 \, \text{feet} \), rounded to four decimal places.

Would you like more details or have any questions?

Here are five related questions to explore:
1. How would the distance change if the angle of elevation were smaller?
2. How do different trigonometric functions relate to angles in right triangles?
3. What is the relationship between height, distance, and angle in real-world applications?
4. How do changes in angle of elevation affect the apparent size of tall objects?
5. How can we measure the height of a tree without knowing the angle of elevation?

**Tip**: When dealing with trigonometry, ensure that the angle is in the correct unit (degrees or radians) before applying trigonometric functions!

Assuming that a 390390-foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be 49°, how far from the base of the tree am I? Round to 4 decimal places.

Find the distance from the base of a 390,390-foot tall tree given an angle of elevation of 49°. This trigonometry problem demonstrates how to use the tangent function to calculate distance. The solution includes step-by-step explanations and is ideal for high school students learning right triangle geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation