Question

Please help ٩(๑òωó๑)۶​

Answer 1

Height of the cliff = 13.66 m

Explanation:

Let the height of the cliff is 'x' m and distance between the base of the cliff and the boat is 'y' m.

From right triangle AOC,

tan 30° =
`\frac{\text{Opposite triangle}}{\text{Adjacent side}}`

`(1)/(√(3))=(x)/(y)`

y =
`x√(3)` ------(1)

From right angle triangle BOC,

tan 45° =
`(x)/(y-10)`

`1=(x)/(y-10)`

x = y - 10

y = x + 10 -------(2)

From equations (1) and (2),

`x√(3)=x+10`

`x(√(3)-1)=10`

`x=(10)/(√(3)-1 )`

x = 13.66 m

Therefore, height of the cliff is 13.66 m.