IB Mathematics Applications & Interpretation Question Type 3: Applying Values of Elevation and Depression Exercises

From the top of a cliff $80\text{ m}$ high, the angle of depression to a ship at sea is $25^{\circ }$. Find the horizontal distance between the cliff base and the ship.

From the top of a lighthouse $60\text{ m}$ above sea level, the angle of depression to a boat is $12^{\circ }$. How far is the boat from the lighthouse horizontally?

A man $2$ m tall stands $30$ m from a building. The angle of elevation to the top of the building from his eyes ($1.6$ m above ground) is $50^{\circ }$. Find the building’s height.

From a point $A$ at the peak of a mountain, the angle of depression to its foot is $35^{\circ }$. From a point $B$ on the mountain slope, $150\text{ m}$ vertically lower than $A$, the angle of depression to the foot is $20^{\circ }$.

Find the vertical height of the mountain (the height of $A$ above its foot).

A 50 m tall tower casts a shadow on level ground such that the angle of elevation of the sun is $37^{\circ }$. Calculate the length of the shadow.

An airplane is flying horizontally at $3000\text{ m}$ altitude. An observer on the ground measures the angle of elevation to the plane as $15^{\circ }$. How far horizontally is the plane from the observer?

An observer moves towards a tower by $40\text{ m}$, and the angle of elevation changes from $20^{\circ }$ to $40^{\circ }$. Find the height of the tower.

A tower stands on level ground. From a point $A$, the angle of elevation to the top is $60^{\circ }$, and from a point $B$ $20\text{ m}$ closer to the tower along the line of sight, the angle is $75^{\circ }$. Find the height of the tower.

A surveyor measures the angle of elevation to the top of a hill from two points, $A$ and $B$, which are $200\text{ m}$ apart on level ground. Points $A$, $B$, and the foot of the hill are collinear and on the same side of the hill. The angle of elevation from the closer point $A$ is $32^{\circ }$ and from the farther point $B$ is $25^{\circ }$. Find the height of the hill relative to the level ground.