Question

cos (52) = 9.2/c
use your trigonometric equation, then solve for c, given m<Y = 52 degrees and b = 9.2
Round to the hundredth place and please dumb it down

Answer 1

To solve the equation \( \cos(52^\circ) = \frac{9.2}{c} \) for \( c \), you can follow these steps:

1. **Understand the equation**: We have the cosine of an angle equal to the fraction \( \frac{9.2}{c} \). Our goal is to find the value of \( c \).

2. **Rearrange the equation to solve for \( c \)**: You can rewrite the equation as:
\[
c = \frac{9.2}{\cos(52^\circ)}
\]

3. **Calculate \( \cos(52^\circ) \)**: You can either use a calculator or a cosine table to find the value of \( \cos(52^\circ) \). The value is approximately:
\[
\cos(52^\circ) \approx 0.6157
\]

4. **Substitute this value back into the equation**:
\[
c = \frac{9.2}{0.6157}
\]

5. **Perform the calculation**:
\[
c \approx \frac{9.2}{0.6157} \approx 14.94
\]

6. **Round to the hundredth place**: The answer, rounded to two decimal places, is:
\[
c \approx 14.94
\]

So, the final answer is \( c \approx 14.94 \).