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Math Help - Trigonometry Problem 3

  1. #1
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    Trigonometry Problem 3

    To calculate the height of a crane which is on top of a building, Denis measures the angle of elevation to the bottom and top of the crane. These were 62 and 68 respectively. If the building is 42 m high find, to 2 decimal places:
    a) how far Denis is from the building
    b) the height of the crane
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  2. #2
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    Quote Originally Posted by Joker37 View Post
    To calculate the height of a crane which is on top of a building, Denis measures the angle of elevation to the bottom and top of the crane. These were 62 and 68 respectively. If the building is 42 m high find, to 2 decimal places:
    a) how far Denis is from the building
    b) the height of the crane
    1. You are dealing with 2 right triangles (see attachment)

    2. \tan(62^\circ)=\dfrac{42}{x} . Solve for x.

    3. The length of the crane is

    x \cdot \tan(68^\circ) - 42 = l_{crane}
    Attached Thumbnails Attached Thumbnails Trigonometry Problem 3-crane_onhouse.png  
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  3. #3
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    Hello, Joker37!

    Did you make a sketch?


    To calculate the height of a crane which is on top of a building,
    Denis measures the angle of elevation to the bottom and top of the crane.
    These were 62 and 68 respectively.
    If the building is 42 m high find, to 2 decimal places:

    a) how far Denis is from the building

    b) the height of the crane.
    Code:
        A o
          |\
          | \
        y |  \
          |   \
          |    \
        B o     \
          | *    \
          |   *   \
       42 |     *6\
          |       * \
          |     62 *\
        C o - - - - - o D
                x
    The crane is AB = y.
    The building is BC = 42.
    Denis is at D\!:\;CD = x
    \angle BDC = 62^o,\;\angle ADC = 68^o


    (a) In right triangle BCD\!:\;\;\tan 62^o \:=\:\frac{42}{x} \quad\Rightarrow\quad x \:=\:\frac{42}{\tan62^o} \;\approx\;22.33 ft.


    (b) In right triangle ACD\!:\;\;\tan68^o \:=\:\frac{y+42}{x} \quad\Rightarrow\quad y \:=\:x\tan68^o - 42 \;\approx\;13.27 ft.


    Edit: Too slow again . . . *sigh*
    .
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