Chapter 9: Some Applications of Trigonometry

Questions

1. Ladder $10$ m at $60^\circ$: height reached.
2. $20$ m tower, elevation $45^\circ$: distance from base.
3. Cliff $100$ m, boat at $30^\circ$ depression.
4. Pole $15$ m, sun $45^\circ$: shadow length.
5. Tree $20$ m tall, sun at $60^\circ$: shadow length.
6. Tower shadow $30$ m, sun $30^\circ$: height.
7. Angles of elevation from a point $10$ m and $40$ m away are complementary. Find height.
8. From top of a $50$ m tower, angle of depression of two objects on ground on same side are $30^\circ$ and $60^\circ$. Find distance between them.
9. A kite is flying at height $60$ m; string makes $60^\circ$ with ground. Length of string?
10. A ladder $\sqrt 3$ m leans against a wall; foot is $1$ m from the wall. Angle with ground?

Extra Practice (Optional)

• A man at $30$ m sees the top of a tower at $60^\circ$. Find tower's height.
• From a boat, an observer sees lighthouse top at $45^\circ$; sailing closer $50$ m, it becomes $60^\circ$. Height?
• Two towers of equal height, $60$ m apart. From middle, elevations $30^\circ$ and $60^\circ$. Heights?
• Balloon at height $88$ m; elevation from a point on ground $30^\circ$; find distance.
• Aeroplane $3000$ m high; elevation changes from $60^\circ$ to $30^\circ$ in $30$ s. Speed?