Answer:
[tex](a)\ AB = \frac{7}{\sin (B)}[/tex] [tex]\to Yes[/tex]
[tex](b)\ AB = \frac{24}{\cos (B)}[/tex] [tex]\to Yes[/tex]
[tex](c)\ AB = \frac{24}{\cos (A)}[/tex] [tex]\to No[/tex]
[tex](d)\ AB = \frac{7}{\cos (A)}[/tex] [tex]\to Yes[/tex]
Step-by-step explanation:
Given
[tex]BC =24[/tex]
[tex]AC = 7[/tex]
Required
Select Yes or No for the given options
[tex](a)\ AB = \frac{7}{\sin (B)}[/tex] [tex]\to Yes[/tex]
Considering the sine of angle B, we have:
[tex]\sin(B) = \frac{Opposite}{Hypotenuse}[/tex]
[tex]\sin(B) = \frac{7}{AB}[/tex]
Make AB, the subject
[tex]AB = \frac{7}{\sin(B)}[/tex]
[tex](b)\ AB = \frac{24}{\cos (B)}[/tex] [tex]\to Yes[/tex]
Considering the cosine of angle B, we have:
[tex]\cos(B) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos(B) = \frac{24}{AB}[/tex]
Make AB the subject
[tex]AB = \frac{24}{\cos(B)}[/tex]
[tex](c)\ AB = \frac{24}{\cos (A)}[/tex] [tex]\to No[/tex]
Considering the cosine of angle B, we have:
[tex]\cos(A) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos(A) = \frac{7}{AB}[/tex]
Make AB the subject
[tex]AB = \frac{7}{\cos(A)}[/tex]
[tex](d)\ AB = \frac{7}{\cos (A)}[/tex] [tex]\to Yes[/tex]
This has been shown in (c) above
