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Urgent help needed my sister has an exam tomorrow!

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    A vertical pole AB stands on horizontal ground

    AB=15

    C is a point due south of B
    D is a point due east of B

    The angle of elevation of A from C is 40
    The angle of elevation of A from D is 35

    Calculate the distance CD Give your answer to 3 significant figures
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    Use triangle ABC to find BC
    Use triangle ABD to find BD

    Use triangle BCD to find CD

    All these are right angled triangles
    In the first 2 you have an angle and a side so use trig
    In the last you have 2 sides so use Pythagoras
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    As stated, you need to 'use triangle ABC to find BC', 'use triangle ABD to find BD and then 'use triangle BCD to find CD'. Here is my working out:

    BC

    tan x°= O/A
    tan 40°= 15/BC
    tan 40°*BC = 15
    BC = 15/tan 40°
    BC = 15/0.839
    BC = 17.876

    BD

    tan x°= O/A
    tan 35°= 15/BD
    tan 35°*BD = 15
    BD = 15/tan 35°
    BD = 15/0.7002
    BD = 21.422

    CD

    a²+b²=c²
    BC²+BD²=CD²
    17.876²+21.422²=CD²
    319.6+458.9=CD²
    778.5=CD²
    √778.5=CD
    27.9=CD
    CD=27.9

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Updated: June 18, 2012
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