Question

the angle of depression of two boats on a river from the top of a tree on the bank of the river 30 degree and 60 degree if the height of the tree is 30 metre and the boats are in the same line with the tree and the one side find the distance between the boats​

Answer 1

Answer:

is 9m

Step-by-step explanation:

Angle of first boat = 60°

Angle of second boat = 75°

Height of pole = 30 m

If we consider triangle formed by first boat and pole then

Distance between boat and pole = d1

And

we know that

tan(α) = height / base

Putting values we get

tan(60) = 30 / d1

d1 = 30 / tan(60) = 17.32 m

Similarly for triangle formed by second boat and pole

Distance between boat and pole = d2

And

we know that

tan(α) = height / base

Putting values we get

tan(75) = 30 / d2

d2 = 30 / tan(75) =8.04 m

And

Distance between boats = 17.32 - 8.04 = 9.28

And nearest meter = 9 m

Answer 2

Angle of first boat = 60°

Angle of second boat = 75°

Height of pole = 30 m

If we consider triangle formed by first boat and pole then

Distance between boat and pole = d1

And

we know that

tan(α) = height / base

Putting values we get

tan(60) = 30 / d1

d1 = 30 / tan(60) = 17.32 m

Similarly for triangle formed by second boat and pole

Distance between boat and pole = d2

And

we know that

tan(α) = height / base

Putting values we get

tan(75) = 30 / d2

d2 = 30 / tan(75) =8.04 m

And

Distance between boats = 17.32 - 8.04 = 9.28

And nearest meter = 9 m