Question

The angle of elevation of the top of an incomplete vertical pillar at a horizontal
distance of 100 meters from its base is 45 degrees. If the angle of elevation
of the top of the complete pillar from the same spot is to be 60 degrees, then
by how much the height of the incomplete pillar should be increased?

Answer 1

Answer:

73.2m

Step-by-step explanation:

∠B=90° as pillar is perpendicular to the ground. Let the top of incomplete tower and complete be C & D respectively. ΔABC and ΔABD ARE right angle triangles.Let AB be y

∴ tan∠CAB=$\frac{perpendicular}{base}$=$\frac{BC}{AB}$ relative to ∠CAB

=tan 45°=$\frac{BC}{AB} =\frac{100}{y}$

⇒1=$\frac{100}{y}$

⇒y=100m=AB

and, tan∠DAB=$\frac{perpendicular}{base}$=$\frac{DB}{AB}$ relative to ∠DAB

⇒tan 60°=$\frac{DB}{AB}=\frac{DB}{100}$

⇒$\sqrt[]{3}=\frac{DB}{100}$

⇒DB=$100\sqrt{3}$

and,DB=DC+BC

⇒DC=DB-BC

=DC=$100\sqrt{3}$-100

=100($\sqrt{3}$-1), taking $\sqrt{3}$ as 1.732

∵DC= 100(1.732-1)=100×0.732=73.2m

∴ the height of the incomplete pillar should be increased by 73.2m.