Question

An aeroplane at an altitude of 250 m observes the angle of depression of two Boats on the opposite banks of a river to be 45° and 60° respectively. Find the width of the river. Write the answer correct to the nearest whole number.

Answer 1

Let the width of the river CD be x,

In ΔABC, 
tan 60° = `"AB"/"BC"`

√3 = `250/"BC"`

BC = `250/sqrt3 xx sqrt3/sqrt3`

BC = `(250/3)sqrt3`        .....(i)

In Δ ABD,

tan 45° = `"AB"/"BD"`

⇒ AB = BD = 250        ....(ii)

∴ BD = BC + CD

∴ 250 = `(250/3) sqrt3 + x`        ....(using (i) and (ii))

∴ x = 250 - `(250/3) xx 1.732`

∴ x = 250 - 83.33 x 1.732

∴ x = 250 - 144.33

∴ x = 105.67 m

∴ x = 106 m   .....(to the nearest whole numbers)

Thus, width of the river is 106 m.