NCERT Example 6 — Some Applications of Trigonometry

NCERT Example

Example 6

angles of depression · two buildings

The angles of depression of the top and bottom of an 8 m building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the buildings.

An 8 metre building AB and multi-storeyed building PC with 30 and 45 degree angles of depression. — Figure 9-9 from the supplied NCERT chapter.

Solution

Board-exam working:

Let PD = x m. Since AB = DC = 8 m, the total height PC = x + 8 m.

In triangle PBD:

\tan30^\circ=\frac{PD}{BD}

\frac1{\sqrt3}=\frac{x}{BD}

BD=x\sqrt3\qquad\text{(1)}

In triangle PAC:

\tan45^\circ=\frac{PC}{AC}=1

AC=PC=x+8\qquad\text{(2)}

The distance between the buildings is the same, so AC = BD.

x+8=x\sqrt3

x(\sqrt3-1)=8

x=\frac8{\sqrt3-1}=4(\sqrt3+1)

PC=x+8=4(\sqrt3+3)\text{ m}

AC=4(\sqrt3+3)\text{ m}

Final answer

Height of the multi-storeyed building = 4(√3 + 3) m; distance between the buildings = 4(√3 + 3) m.

Example 6

Example 6

Solution

Final answer

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