A 10-foot ladder is leaning against a house.  It reaches 8 feet up the house.  What is the measure of the angle formed by the base of the ladder and the ground?  Assume the ground is horizontal and the house is vertical.  Round to two decimal places, if necessary.

We can solve this problem using trigonometry. In this scenario, we can treat the ladder, the height it reaches up the house, and the distance of the base of the ladder from the house as a right triangle.

### Given:
- Length of the ladder (hypotenuse) = 10 feet
- Height up the house (opposite side) = 8 feet

We need to find the angle between the ladder and the ground, which is adjacent to the base of the triangle.

To do this, we use the sine function, which relates the opposite side to the hypotenuse:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{10} = 0.8
\]
Now, to find the angle \(\theta\), take the inverse sine (\(\sin^{-1}\)) of 0.8:
\[
\theta = \sin^{-1}(0.8)
\]

Using a calculator:
\[
\theta \approx 53.13^\circ
\]

So, the measure of the angle formed by the base of the ladder and the ground is approximately **53.13 degrees**.

Would you like further details or have any other questions?

Here are 5 related questions you could explore:
1. What is the distance from the base of the ladder to the wall?
2. If the ladder reached 9 feet up the house, what would the new angle be?
3. What would the angle be if the ladder was 12 feet long, but still reached 8 feet up?
4. Can you calculate the cosine of the angle formed by the ladder and the ground?
5. How would you determine the angle if the ladder reached exactly half its length up the wall?

**Tip:** Remember, in any right triangle, the sine function is useful when you know the opposite side and the hypotenuse.

A 10-foot ladder is leaning against a house. It reaches 8 feet up the house. What is the measure of the angle formed by the base of the ladder and the ground? Assume the ground is horizontal and the house is vertical. Round to two decimal places, if necessary.

Solve a real-world trigonometry problem where a 10-foot ladder leans against a house and reaches 8 feet up. Learn how to calculate the angle between the ladder and the ground using the sine function, providing a step-by-step solution. Suitable for students in Grades 9-10.

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