To solve for [tex]\( x \)[/tex] in the equation [tex]\( x = 19 \cdot \sin 28^\circ \)[/tex] and round to the nearest tenth, follow these detailed steps:
1. Understanding the Problem:
- We begin with the equation [tex]\( x = 19 \cdot \sin 28^\circ \)[/tex].
- Our goal is to find the value of [tex]\( x \)[/tex] after calculating [tex]\( 19 \cdot \sin 28^\circ \)[/tex].
- Finally, we round the result to the nearest tenth.
2. Calculate [tex]\( 19 \cdot \sin 28^\circ \)[/tex]:
- The problem provides us with the value of [tex]\( \sin 28^\circ \approx 0.4694716 \)[/tex].
- Multiply this value by 19 to find [tex]\( x \)[/tex].
3. Perform the Multiplication:
- [tex]\( 19 \cdot 0.4694716 = 8.9199596 \)[/tex].
- So, [tex]\( x = 8.9199596 \)[/tex].
4. Rounding to the Nearest Tenth:
- To round [tex]\( 8.9199596 \)[/tex] to the nearest tenth, look at the digit in the hundredths place, which is 1.
- Since 1 is less than 5, we round down the digit in the tenths place.
- Therefore, [tex]\( 8.9199596 \)[/tex] rounded to the nearest tenth is [tex]\( 8.9 \)[/tex].
5. Conclusion:
- The calculated value is [tex]\( 8.9199596 \)[/tex].
- After rounding, the approximate value of [tex]\( x \)[/tex] is [tex]\( 8.9 \)[/tex].
So, the solution is that [tex]\( x \)[/tex] rounds to [tex]\( 8.9 \)[/tex] when rounded to the nearest tenth.
