Question

Please help ٩(๑òωó๑)۶​

Answer 1

Answer:

Height of the cliff = 13.66 m

Step-by-step 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° = $\frac{\text{Opposite triangle}}{\text{Adjacent side}}$

$\frac{1}{\sqrt{3}}=\frac{x}{y}$

y = $x\sqrt{3}$ ------(1)

From right angle triangle BOC,

tan 45° = $\frac{x}{y-10}$

$1=\frac{x}{y-10}$

x = y - 10

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

From equations (1) and (2),

$x\sqrt{3}=x+10$

$x(\sqrt{3}-1)=10$

$x=\frac{10}{\sqrt{3}-1 }$

x = 13.66 m

Therefore, height of the cliff is 13.66 m.