In the side of a hill that slopes upward at an angle of $32^\circ$, a tunnel is bored sloping downward at an angle of $12^\circ15'$ from the horizontal.
How far below the surface of the hill is a point $38$ meters down the tunnel?
Trigonometry problem: How far below the surface of the hill is a point $38m$ down the tunnel?
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trigonometry
slope
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1What is " 12º15' from the horizontal" – 2017-02-04
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1What have you tried? We don't just *do* random problems without some effort or research on the poster's part. – 2017-02-04
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1The best advice is probably "Draw a diagram". – 2017-02-04
1 Answers
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The horizontal distance from the tunnel entrance at a point $38$m along the tunnel is $h=38\cos(12.25°)$. Then the distance below the tunnel entrance is $v_1=38\sin(12.25°)$ and the corresponding distance of the hillside above that point is $v_2=h\tan(32°)$. The value you want is $v_1+v_2$.
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0Thanks but the issue here is that I can't sketch it – 2017-02-04
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0@HENPAUL added image – 2017-02-04
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0Very grateful, I can complete the working – 2017-02-04
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0@HENPAUL For a future question, please, show a little what you have done on the subject. – 2017-02-04