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The problem asks to find the acute angle that a ladder makes with the ground. Here's how we can approach it:

We know the following:
- The length of the ladder, which is the hypotenuse, \( h = 5.7 \, \text{m} \),
- The horizontal distance from the base of the ladder to the wall, which is the adjacent side, \( a = 1.5 \, \text{m} \).

To find the acute angle \( \theta \) between the ladder and the ground, we use the trigonometric relationship:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{a}{h}
\]

So:
\[
\cos(\theta) = \frac{1.5}{5.7}
\]

Now, we'll calculate \( \theta \) using the inverse cosine function:
\[
\theta = \cos^{-1} \left( \frac{1.5}{5.7} \right)
\]

Let me calculate the value.The acute angle that the ladder makes with the ground is approximately \( 74.7^\circ \) (to 1 decimal place).

Would you like more details on any part of the solution, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. How would you calculate the height at which the ladder touches the wall?
2. What would change if the base of the ladder were moved closer or farther from the wall?
3. How would you find the other acute angle in this right triangle?
4. How can you verify the result using the sine or tangent functions?
5. How does the angle change if the length of the ladder is increased?

**Tip:** In right-angle trigonometry, knowing any two sides of a right triangle allows you to calculate all angles and sides.

A 5.7 m long ladder is leaning against a wall. The wall stands perpendicular to the ground. The base of the ladder is 1.5 m away from the wall. Work out the size of the acute angle that the ladder makes with the ground. Give your answer in degrees to 1 d.p.

Learn how to calculate the acute angle a ladder makes with the ground using trigonometry. The ladder is 5.7 m long and its base is 1.5 m away from the wall. Find the angle using the cosine formula. Suitable for students in Grades 9-10.

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