Question

From a point across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 5m from the banks, find the width of river.​

Answer 1

Answer:

ANSWER

In figure, A and B are points on th bank on opposite sides of river.

⇒ AB is the width of the river.

P is the point on bridge at a height =30m i.e. DP=30m

Now, AB=AD+DB

In right angled △ADP,

∠A=30

o

⇒ tan30

o

=

AD

PD

⇒

3

1

=

AD

30

∴ AD=30

3

m

In right angled △PDB,

tan45

o

=

DB

PD

⇒ 1=

DB

30

∴ DB=30m

Now, AB=BD+AD=30+30

3

m=30+30(1.732)=81.96m

∴ The width of river is 81.96m

Answer 2

refer the 3 attachment above