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Svetlanka [38]
3 years ago
15

Determine whether each expression can be used to find the length of side AB. Match Yes or No for each

Mathematics
1 answer:
tankabanditka [31]3 years ago
3 0

Answer:

(a)\ AB = \frac{7}{\sin (B)}  \to Yes

(b)\ AB = \frac{24}{\cos (B)} \to Yes

(c)\ AB = \frac{24}{\cos (A)} \to No

(d)\ AB = \frac{7}{\cos (A)}  \to Yes

Step-by-step explanation:

Given

BC =24

AC = 7

Required

Select Yes or No for the given options

(a)\ AB = \frac{7}{\sin (B)}  \to Yes

Considering the sine of angle B, we have:

\sin(B) = \frac{Opposite}{Hypotenuse}

\sin(B) = \frac{7}{AB}

Make AB, the subject

AB = \frac{7}{\sin(B)}

(b)\ AB = \frac{24}{\cos (B)} \to Yes

Considering the cosine of angle B, we have:

\cos(B) = \frac{Adjacent}{Hypotenuse}

\cos(B) = \frac{24}{AB}

Make AB the subject

AB = \frac{24}{\cos(B)}

(c)\ AB = \frac{24}{\cos (A)} \to No

Considering the cosine of angle B, we have:

\cos(A) = \frac{Adjacent}{Hypotenuse}

\cos(A) = \frac{7}{AB}

Make AB the subject

AB = \frac{7}{\cos(A)}

(d)\ AB = \frac{7}{\cos (A)}  \to Yes

<em>This has been shown in (c) above</em>

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