https://file.aiquickdraw.com/mathbot/file/1728564942413zowopv6i.jpg

To solve this problem, we need to find the angle \(\theta\) of the slope using the rise and run provided:

- **Rise (Opposite side):** \(15 \, \text{cm}\)
- **Run (Adjacent side):** \(2 \, \text{m} = 200 \, \text{cm}\)

Since the problem involves a right-angled triangle, we can use the tangent function:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{15}{200}
\]

Now, we need to find \(\theta\):

\[
\theta = \arctan\left(\frac{15}{200}\right)
\]

Let's calculate this:

\[
\theta \approx \arctan(0.075) \approx 4.29^\circ
\]

Rounded to the nearest degree, \(\theta\) is approximately **4°**.

Would you like more details on the steps or have any questions?

Here are 5 related questions for further understanding:

1. How do you convert radians to degrees when calculating angles?
2. What other trigonometric functions could we use to find \(\theta\) if we knew the hypotenuse?
3. How would the angle change if the rise was doubled while keeping the run constant?
4. What does the value of \(\tan(\theta)\) represent in this context?
5. How can we use trigonometry to find the length of the hypotenuse in this problem?

**Tip:** When solving trigonometric problems, always ensure the units are consistent before performing calculations.

A road rises 15 cm for every 2 m travelled horizontally. Find the angle of slope θ to the nearest degree.

This problem involves finding the angle of a slope for a road that rises 15 cm for every 2 meters travelled horizontally. Using trigonometric principles and the tangent function, we calculate the angle to be approximately 4°. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation