To solve the equation [tex]\( p \sin 70^\circ = 9 \)[/tex] for the value of [tex]\( p \)[/tex], follow these steps:
1. Understand the equation: The given equation is [tex]\( p \sin 70^\circ = 9 \)[/tex]. We are interested in solving for [tex]\( p \)[/tex].
2. Rearrange the equation: To isolate [tex]\( p \)[/tex], divide both sides of the equation by [tex]\( \sin 70^\circ \)[/tex]:
[tex]\[
p = \frac{9}{\sin 70^\circ}
\][/tex]
3. Calculate [tex]\( \sin 70^\circ \)[/tex]: The value of [tex]\( \sin 70^\circ \)[/tex] is approximately 0.9397.
4. Divide 9 by [tex]\( \sin 70^\circ \)[/tex]: Use the value of [tex]\( \sin 70^\circ \)[/tex] to find [tex]\( p \)[/tex]:
[tex]\[
p = \frac{9}{0.9397}
\][/tex]
[tex]\[
p \approx 9.57759995228321
\][/tex]
5. Round to 2 decimal places: The value of [tex]\( p \)[/tex] should be rounded to two decimal places:
[tex]\[
p \approx 9.58
\][/tex]
So, the value of [tex]\( p \)[/tex] rounded to 2 decimal places is [tex]\( 9.58 \)[/tex].
