NCERT Example 7 — Some Applications of Trigonometry

NCERT Example

Example 7

bridge · angles of depression

From a point on a bridge across a river, the angles of depression of the opposite banks are 30° and 45°. If the bridge is 3 m above the banks, find the width of the river.

Bridge point P three metres above river banks A and B, with angles of depression 30 and 45 degrees. — Figure 9-10 from the supplied NCERT chapter.

Solution

Board-exam working:

Let P be the observation point and PD = 3 m. The river width is AB = AD + DB.

In triangle APD:

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

\frac1{\sqrt3}=\frac3{AD}

AD=3\sqrt3\text{ m}

In triangle PBD:

\tan45^\circ=\frac{PD}{DB}

1=\frac3{DB}

DB=3\text{ m}

AB=AD+DB=3\sqrt3+3=3(\sqrt3+1)\text{ m}

Final answer

The river is 3(√3 + 1) m wide.