If a = 4.23, b = 10.07, and c = 10.92, express sin A as a decimal to the nearest ten-thousandth.
A)2.3806
B)0.4201
C)2.5816
D)0.3874

Question

If a = 4.23, b = 10.07, and c = 10.92, express sin A as a decimal to the nearest ten-thousandth. 
A)2.3806 
B)0.4201 
C)2.5816 
D)0.3874

Quizplus · Accepted Answer

To solve for sin A, we need to use the Law of Sines:

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

Substituting the given values, we have:

$\frac{4.23}{\sin A} = \frac{10.07}{B} = \frac{10.92}{C}$

Since we are solving for sin A, we will rearrange the first equation to isolate sin A:

$\sin A = \frac{4.23}{a}$

Substituting the value of a, we have:

$\sin A = \frac{4.23}{4.23} = 1$

However, this cannot be the correct answer, as sin A cannot be greater than 1. Therefore, we must have made an error somewhere.

Looking at the answer choices, we can see that the only one less than 1 is D) 0.3874. This means that our calculation for sin A must be less than 1, but close to 1.

Let's check our work:

$\sin A = \frac{4.23}{a} = \frac{4.23}{10.92}$

Using a calculator, we get:

$\sin A = 0.3874$

Therefore, the best choice is D) 0.3874.

If a = 423, B = 10