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In traveling across flat land, you notice a mountain in front of you. Its angle of elevation to the peak is 3.5 degrees. After you drive 13 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain.

  • MATH -

    make a sketch
    draw the height of the mountain as AB
    C is the point of first observation (3.5°)
    D is the point of second observation (9°)
    angle B = 90° , CD=13, angle C=3.5, and angle ADB=9°

    In triangle ACD, angle CDA = 171° and angle CAD=5.5°
    by the Sine Law:
    AD/sin 3.5 = 13/sin 5.5
    AD = 13sin3.5/sin5.5 = 8.28029

    now in the right-angled triangle,
    sin 9° = AB/AD
    AB =8.28029sin9 = 1.295 miles

    check my arithmetic

  • MATH -

    Thank you so much! I was stuck on that one

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