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Allisa [31]
3 years ago
14

In the figure below, A shows the position of a house on the shore and B shows the position of a house on an island. To find the

distance between the two houses,a surveyor measures from the house on shore to point C. An instrument is used to find

Mathematics
1 answer:
sashaice [31]3 years ago
5 0

Question

In the figure below, A shows the position of a house on the shore and B shows the position of a house on an island. To find the distance between the two houses,a surveyor measures from the house on shore to point C. An instrument is used to find

Answer:

The Answer is A and B is  70 m away


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Answer:

See Explanation

Step-by-step explanation:

\frac{ \sin5A}{\sin A}  -  \frac{ \cos5A}{\cos A}  = 4\cos2A \\  \\ LHS = \frac{ \sin5A}{\sin A}  -  \frac{ \cos5A}{\cos A}   \\  \\  =  \frac{ \sin5A \:\cos A -  \cos5A \:  \sin A}{\sin A \:\cos A }  \\  \\  =  \frac{ \sin(5A -A )}{\sin A \:\cos A}  \\  \\ =  \frac{ \sin 4A}{\sin A \:\cos A}  \\  \\ =  \frac{ 2\sin 2A \: \cos 2A}{\sin A \:\cos A}  \\  \\ =  \frac{ 2 \times 2\sin A \: \cos A \: \cos 2A}{\sin A \:\cos A}  \\  \\ =  \frac{ 4\sin A \: \cos A \: \cos 2A}{\sin A \:\cos A}  \\  \\ =4\cos 2A \\  \\  = RHS \\  \\ thus \\  \\  \frac{ \sin5A}{\sin A}  -  \frac{ \cos5A}{\cos A}  = 4\cos2A \\  \\ hence \: proved

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