A boat is 120 m from the foot of a cliff. The angle of depression from the top of the cliff to the boat is 60 degrees. Calculate the height of the cliff.

Here are the solutions to the assignment questions from the image:

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Let $H$ be the height of the cliff.
Let $D$ be the distance of the boat from the foot of the cliff. We are given $D = 120$ m.
The angle of depression from the top of the cliff to the boat is $60^\circ$. This means the angle of elevation from the boat to the top of the cliff is also $60^\circ$.

Step 1: Set up the trigonometric relationship.
Using the tangent function for the right-angled triangle:

$$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ $$\tan(60^\circ) = \frac{H}{D}$$

Step 2: Substitute the given values and solve for $H$.

$$\tan(60^\circ) = \frac{H}{120}$$ $$H = 120 \tan(60^\circ)$$ $$H = 120 \times \sqrt{3}$$ $$H \approx 120 \times 1.7320508$$ $$$$