From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff. (Take √3= 1.732)

Given : Height of building = BC = 10 m

$$\angle$$BPC = 30° and $$\angle$$APC = 45°

To find : length of flagstaff = AB = ?

Solution : In $$\triangle$$BCP

=> $$tan 30^{\circ} = \frac{BC}{CP}$$

=> $$\frac{1}{\sqrt{3}} = \frac{10}{CP}$$

=> $$CP = 10\sqrt{3}$$

Now, in $$\triangle$$ACP

=> $$tan 45^{\circ} = \frac{AC}{CP}$$

=> $$1 = \frac{AC}{10\sqrt{3}}$$

=> $$AC = 10\sqrt{3}$$

Now, AB = AC - BC

=> $$AB = 10\sqrt{3} - 10$$

=> $$AB = 17.32-10 = 7.32 m$$