To find angle A using the Law of Sines, we can set up the ratio involving the sides opposite the angles. The Law of Sines states that:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
In the triangle ABC that you described, we know:
- \( a = 10 \) (opposite angle A)
- \( b = 15 \) (opposite angle B, which is 85 degrees)
- Angle C is 40 degrees
To find angle A, we can write:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} \]
Substituting in our known values:
\[ \frac{10}{\sin A} = \frac{15}{\sin 85^\circ} \]
Rearranging gives:
\[ \frac{\sin A}{10} = \frac{\sin 85^\circ}{15} \]
Thus, the correct ratio that helps find the value of angle A is:
\[ \frac{\sin A}{10} = \frac{\sin 85^\circ}{15} \]
So the correct response is:
Start Fraction sine upper A over 10 End Fraction equals Start Fraction sine 85 degrees over 15 End Fraction