Question

A cat is trapped in a tree and a ladder is placed against the tree to rescue it. The ladder rests against the tree making an angle of 60 degrees with the horizontal and reaching 14 metres up the tree, allowing the rescuer to reach the cat. Just as the cat is about to be rescued, it jumps to a branch 1 metre above its original resting place. Calculate the size of the angle, to the nearest degree, that the ladder now must make with the horizontal to allow the rescuer to reach the cat. Remember to show calculations.

Answer 1

To rescue the cat that jumped to a branch 1 metre above its original resting place, the ladder now needs to make an angle of approximately 47 degrees with the horizontal.

Step-by-step explanation:

To calculate the angle that the ladder must now make with the horizontal, we can use trigonometry.

Since the rescuer is 1 metre above the original resting place of the cat, the height the ladder needs to reach is now 14 + 1 = 15 metres.

We can use the sine function to find the angle.

Sin(θ) = opposite/hypotenuse, so sin(θ) = 15/14 = 1.071.

Taking the inverse sine of this value gives us θ = 47 degrees (rounded to the nearest degree).