Use the diagram, which is not drawn to scale to find AD if you know that AC=24 & BC=12a.6b.18c.16.97d.20.78

Accepted Solution

Answer:Option b. [tex]AD=18\ units[/tex]Step-by-step explanation:step 1In the right triangle ABCFind the sine of angle CAB[tex]sin(<CAB)=\frac{BC}{AC}[/tex] ---> the sine of angle CAB is equal to divide the opposite side angle CAB (BC) by the hypotenuse (AC)substitute[tex]sin(<CAB)=\frac{12}{24}[/tex] simplify[tex]sin(<CAB)=\frac{1}{2}[/tex] ---->equation Astep 2In the right triangle BDCFind the sine of angle CBD[tex]sin(<CBD)=\frac{DC}{BC}[/tex] ---> the sine of angle CBD is equal to divide the opposite side angle CBD (DC) by the hypotenuse (BC)substitute[tex]sin(<CBD)=\frac{DC}{12}[/tex] ----> equation Bstep 3we know thatIf two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruentIn this problem Triangles ABC and BDC are similar by AA Similarity Theoremthereforem∠CBD≅m∠CABequate equation A and equation B[tex]\frac{DC}{12}=\frac{1}{2}[/tex] solve for DC[tex]DC=\frac{12}{2}=6\ units[/tex] step 4Find the value of AD[tex]AD=AC-DC[/tex]substitute the values[tex]AD=24-6=18\ units[/tex]