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?
2026-03-25 21:49:02.1774475342
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 $v_1+v_2$.