Question

solve for p, rounded to the nearest whole number.
$p = 24$
$p = 47$
$p = 43$
$p = 66$

Explanation:

Step1: Use trigonometric ratio

In a right - angled triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, for angle \(p\), \(\sin p=\frac{11}{\sqrt{11^{2}+12^{2}}}\) (but it's easier to use \(\tan p=\frac{\text{opposite}}{\text{adjacent}}\) is wrong. Correct: \(\sin p=\frac{11}{\sqrt{11^{2} + 12^{2}}}\) is complex. Use \(\sin p=\frac{11}{\sqrt{11^{2}+12^{2}}}\) is not the best. Use \(\sin p=\frac{11}{\sqrt{11^{2}+12^{2}}}\) is wrong approach. Correct: Since it's a right - angled triangle, \(\sin p=\frac{\text{opposite}}{\text{hypotenuse}}\). The hypotenuse \(h=\sqrt{11^{2}+12^{2}}=\sqrt{121 + 144}=\sqrt{265}\approx16.28\). \(\sin p=\frac{11}{16.28}\approx0.676\).

Step2: Find the angle

\(p=\sin^{- 1}(0.676)\approx42.5^{\circ}\approx43^{\circ}\) (rounded to the nearest whole number)

Answer:

C. \( p = 43 \)