A D ‾ \overline{AD}

Geometry Level 3

It is given that A B ‾ = 7.7 units \overline{AB}=\SI{7.7}{units} , ∠ C A B = 36 ° \angle CAB=36\degree , B C ‾ = 9 units \overline{BC}=\SI{9}{units} and ∠ A C D = ∠ B C D = θ \angle ACD=\angle BCD=\theta .

Find A D ‾ \overline{AD} (in units \text{units} ).


The answer is 4.69.

Gandoff Tan by Gandoff Tan , 19, Singapore

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1 solution

Applying Sine rule to the △ A B C \triangle ABC we get θ = 15.09545 ° \theta =15.09545\degree . Applying Sine rule to the △ B D C \triangle BDC we get 7.7 − A D ‾ s i n θ = 9 s i n ( 36 ° + θ ) \dfrac{7.7-\overline {AD}}{sin \theta}=\dfrac{9}{sin (36\degree+\theta)} , or A D ‾ = 4.688 \overline {AD}=\boxed {4.688}

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Is there any other way to solve this problem without using trigonometric functions?

Sonali Mate - 1 year, 7 months ago

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