Question

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In the figure below AB and CD are perpendicular to BC and the size of angle ACB is 31°. Find the length of segment BD. ​

Answer 1

Use right triangle ABC to write:

tan(31°) = 6 / BC ,

solve:

BC = 6 / tan(31°)

Use Pythagora's theorem in the right

triangle BCD to write:

92 + BC2 = BD2

Solve above for BD and substitute BC:

BD = √ [ 9 + ( 6 / tan(31°) )2 ]

= 13.4 (rounded to 3 significant digits)

Answer 2

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$\mathfrak{The\:Answer\:is}$

Use right triangle ABC to write: tan(31°) = 6 / BC , solve: BC = 6 / tan(31°)

Use Pythagora's theorem in the right triangle BCD to write:

92 + BC2 = BD2

Solve above for BD and substitute BC: BD = √ [ 9 + ( 6 / tan(31°) )2 ]

= 13.4 (rounded to 3 significant digits)

$\boxed{Hope\:This\:Helps}$

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