Question Type 3: Applying values of elevation and depression Exercises

From the top of a $50 \text{ m}$ tall building, the angle of depression to a car on the adjacent road is $45^\circ$. Determine the horizontal distance from the building's base to the car.

A boat observes the top of a lighthouse at an angle of elevation of $20^\circ$. The lighthouse is $50 \text{ m}$ tall. Estimate the horizontal distance from the boat to the lighthouse base.

A surveillance camera is mounted $10 \, \text{m}$ above the ground and tilts downward at an angle of depression of $25^\circ$ to cover an area. Calculate how far along the ground from the base of the camera the view reaches.

A man of height $1.6 \text{ m}$ stands $20 \text{ m}$ from a vertical tower. The angle of elevation from his eyes to the top of the tower is $30^\circ$. Determine the height of the tower.

Two buildings of heights $50 \text{ m}$ and $30 \text{ m}$ stand $100 \text{ m}$ apart. From the top of the shorter building, find the angle of elevation to the top of the taller building.

From the top of a tower $50 \text{ m}$ high, the angle of depression to a point on level ground is $30^\circ$. Find the horizontal distance from the base of the tower to that point.

From a point on level ground, the angle of elevation to the top of a vertical tower of height $50 \text{ m}$ is $60^\circ$. Calculate the horizontal distance from the point to the base of the tower.

From the deck of a ship, an observer $5 \text{ m}$ above sea level measures the angle of depression to a buoy as $15^\circ$. Find the direct line-of-sight distance between the observer and the buoy.

Find the height of the tree.

From point A, the angle of elevation to the top of a tower is $50^\circ$. From point B, on the same level ground, due south of A and $100\text{ m}$ from A, the angle of elevation is $40^\circ$. Given that points A, B, and the base of the tower are collinear, determine the height of the tower.