Question

If $\theta$ is an acute angle and $sin\theta =\frac{p-6}{8-p},$ then p must satisfy

• A. $6\le p$ < 8
• B. $6\le p$ < 7
• C. $3\le p\le 4$
• D. $4\le p$ < 7

Answer 1

The correct option is B $6\le p$ < 7

$\theta$ is an acute angle so $0^{\circ }\le \theta <{90}^{\circ }$
$\therefore 0\le \frac{p-6}{8-p}$ < 1 $\Rightarrow 0\le (p-6)$ < $(8-p)\Rightarrow 6\le p$ < 7.