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Natali [406]
3 years ago
13

Sin150+sin120÷cos210-cos300

Mathematics
1 answer:
natulia [17]3 years ago
6 0
From sin(180-x) = sin(x)
sin(150) = sin(180-30) = sin(30)
sin(120) = sin(180-60) = sin(60)

from cos(360-x) = cos(x)
cos(300) = cos(360-60) = cos(60)
cos(210) = cos(360-150) = cos(150)

from cos(180-x) = -cos(x)
cos(210) = cos(150) = cos(180-30) = -cos(30)
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A tunnel is 300 feet deep and makes an angle of 30 with the ground .
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Answer:

\boxed{C.\:\: 600\:feet}

Step-by-step explanation:


The tunnel, the ground and the depth of the tunnel form a right angle triangle.

The length of the tunnel is the hypotenuse of the right triangle that has been formed.


Let the length of the tunnel be m\: feet.


Using the sine ratio, we obtain;


\sin(30\degree)=\frac{Opposite}{Hypotenuse}


The length of the opposite side is 300\:feet


We substitute the given values to obtain;


\sin(30\degree)=\frac{300}{m}


\Rightarrow \frac{1}{2}=\frac{300}{m}


We cross multiply to obtain;


m=300\times2


m=600\:feet


Therefore the correct answer is C.


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