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kumpel [21]
4 years ago
8

Please help ٩(๑òωó๑)۶​

Mathematics
1 answer:
otez555 [7]4 years ago
7 0

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.

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