Trigonometry problem: How far below the surface of the hill is a point $38m$ down the tunnel?

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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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HENPAUL
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HENPAUL

I am a teacher from Nigeria, study mathematics

Updated on December 09, 2022

Comments

  • HENPAUL
    HENPAUL 11 months

    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?

    • K Split X
      K Split X almost 7 years
      What is " 12º15' from the horizontal"
    • The Count
      The Count almost 7 years
      What have you tried? We don't just do random problems without some effort or research on the poster's part.
    • Joffan
      Joffan almost 7 years
      The best advice is probably "Draw a diagram".
  • HENPAUL
    HENPAUL almost 7 years
    Thanks but the issue here is that I can't sketch it
  • Joffan
    Joffan almost 7 years
    @HENPAUL added image
  • HENPAUL
    HENPAUL almost 7 years
    Very grateful, I can complete the working
  • Jean Marie
    Jean Marie almost 7 years
    @HENPAUL For a future question, please, show a little what you have done on the subject.