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In the diagram, ∠ABC = ∠BDC = 90◦. We know BD = 30 and CD = 72. What is AB?

 Dec 20, 2022
 #1
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By sine law,

AB = AD*sin(angle BAD)/sin(ABD) = BD/sin(BCD)*sin(BDC) = 30/72*24 = 10

 Dec 20, 2022
 #2
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In right triangle DBC, the sides are: BC==78, BD==30,  DC==72. Angle BDC==90, Angle DBC==67.38, Angle BCD ==22.62 degrees

 

In right triangle ABD, the angles are: BDA==90,  DBA==22.62,  DAB==67.38

 

Sine(67.38) ==30 / AB

0.923076 ==30 / AB

AB ==30 / 0.923076

AB ==32.50

 Dec 21, 2022

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