91Ó°ÊÓ

A flagstaff of \(5 \mathrm{~m}\) high stands on a building of \(25 \mathrm{~m}\) high. The flagstaff and the building subtends equal angles at a point \(P, 30 \mathrm{~m}\) high above the ground. Find the distance of \(P\) from the top of flagstaff.

An object is observed from three points \(A, B, C\) lying in a horizontal straight line which passes directly underneath the object. The angular elevation at \(B\) is twice that at \(A\) and at \(C\) three times at \(A\). If \(A B=a, B C=b\), find the height of the object.

From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to \(45^{\circ}\) and \(60^{\circ}\). Then the height in miles of aeroplane above the road is (a) \(\frac{\sqrt{3}}{\sqrt{3}+1}\) (b) \(\frac{\sqrt{3}}{\sqrt{3}-1}\)

A man notices two objects in a striaght line due west of him. After walking a distance \(c\) due north he observes that the objects subtend an angle \(\alpha\) at his eye and after walking a further distance \(c\) due north, an angle \(\beta\). Find the distance between the objects.

\(A B\) is a vertical tower ' \(A\) ' being its foot standing on a horizontal ground. ' \(C\) ' is the mid-point of \(A B\). Portion \(C B\) subtends an angle \(\theta\) at the point \(P\) on the ground. If \(A P=2 A B\), then find \(\tan (\theta)\).

The angle of elevation of an aeroplane from a point 200 meters above a lake is \(45^{\circ}\) and the angle of depression of its replection is \(75^{\circ} .\) Find the height of the aeroplane above the surface of the lake.

At the foot of a mountain the elevation of its peak is found to be \(\frac{\pi}{4}\), after ascending \(10 \mathrm{~m}\) toward the mountain up a slope of \(\frac{\pi}{6}\) inclination, the elevation is found to be \(\frac{\pi}{3}\). Find the height of the mountain.

From the bottom of a pole of height \(h\), the angle of elevation of the top of a tower is \(\alpha .\) The pole subtends an angle \(\beta\) at the top of the tower. Find the height of the tower.

A man finds that at a point due south of a vertical tower the angle of elevation of the tower is \(\frac{\pi}{3}\). He then walks due west \(10 \sqrt{6} \mathrm{~m}\) on the horizontal plane and find the angle of elevation of the tower to be \(\frac{\pi}{6}\). Find the original distance of the man from the tower.

The angle of elevation of the top of vertical tower from a point \(A\) on the horizontal ground is found tobe \(\frac{\pi}{4}\). From ' \(A\) ' a man walks \(10 \mathrm{~m}\) up a path sloping at an angle \(\pi / 6\). After this the slope becomes steeper and after walking up another \(10 \mathrm{~m}\), the man reaches the top of the tower. Find the distance of ' \(A\) ' from the foot of the tower.