Question

Can you please explain the correct answer

Answer 1

 For this case we have as data:
 1) hypotenuse of the triangle
 2) Angle between the base of the triangle and the hypotenuse.
 Therefore, we can use the following trigonometric relationship:
 $sine (40) = AC / 10$
 From here, we clear the value of AC.
 We have then:
 $AC = 10 * sine (40)$
 Answer:
 The encuacion that can be used to find the length of AC is given by:
 $AC = 10 * sine (40)$
 option 1

Answer 2

Answer:

(A)$AC=10sin40^{\circ}$

Step-by-step explanation:

From the given figure, it is given that ABC is a right angled triangle which is right angled at C and AC=b, CB=a and AB=10in.

Now, using the trigonometry, we have

$\frac{AC}{AB}=sinB$

Substituting the given values, we have

$\frac{AC}{10}=sin40^{\circ}$

$AC=10sin40^{\circ}$

Thus, the above equation can be used to find the value of AC, therefore

⇒$b=10sin40^{\circ}$

⇒$b=10(0.642)$

⇒$b=6.42 in$

Thus, the value of AC is 6.42 inches.