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° = [tex]\frac{\text{Opposite triangle}}{\text{Adjacent side}}[/tex]
[tex]\frac{1}{\sqrt{3}}=\frac{x}{y}[/tex]
y = [tex]x\sqrt{3}[/tex] ------(1)
From right angle triangle BOC,
tan 45° = [tex]\frac{x}{y-10}[/tex]
[tex]1=\frac{x}{y-10}[/tex]
x = y - 10
y = x + 10 -------(2)
From equations (1) and (2),
[tex]x\sqrt{3}=x+10[/tex]
[tex]x(\sqrt{3}-1)=10[/tex]
[tex]x=\frac{10}{\sqrt{3}-1 }[/tex]
x = 13.66 m
Therefore, height of the cliff is 13.66 m.
