Chapter 4 - Section 4.8 - Applications of Trigonometric Functions - Exercise Set - Page 637: 3

$ a=42.90; b=32.79; B=37.4^{\circ}$

Here, we have $ A=41.5^{\circ}$ ; $ b= 20$ Since, $\sin \theta= \dfrac{height}{hypotenuse}$ $ a=54\sin 52.6^{\circ} =42.90$ Now, $ b=54 \cos 52.6^{\circ}=32.79$ So, $ B=90^{\circ} - 52.6^{\circ}=37.4^{\circ}$ Thus, $ a=42.90; b=32.79; B=37.4^{\circ}$