b) Similar triangles have corresponding c) The cosine of an acute angle in a right to the hypotenuse. d) In any right triangle, the sum of the $s q$ e) None of these 3. Which of the following triangles would you a) $m=11, n=13, p=16$ b) $r=23, T=47^{\circ}, R=63^{\circ}$ c) $h=6.9, j=7.8, K=109^{\circ}$ d) $R=65^{\circ}, p=12, q=15$ e) None of the above 4. An all-terrain vehicle travels $4 \mathrm{~km}$ due south and angle formed between the two legs of the journey. b) $20^{\circ}$ c) $70^{\circ}$ d) $110^{\circ}$ e) None of these 5. $\sin 63^{\circ}$ is equal to: a) $\sin 117^{\circ}$ b) $\cos 63^{\circ}$ d) $\sin 27^{\circ}$ e) None of these

Step 1 ：Check if the given values form a valid triangle. For sides, the sum of any two sides should be greater than the third side. For angles, the sum should be equal to 180 degrees.

Step 2 ：Valid triangles are: (a) $m=11, n=13, p=16$, (b) $r=23, T=47^{circ}, R=63^{circ}$, (c) $h=6.9, j=7.8, K=109^{circ}$, and (d) $R=65^{circ}, p=12, q=15$.

Step 3 ：\(\boxed{\text{All the given triangles (a, b, c, and d) are valid.}}\)

Step 4 ：Question 4 cannot be answered with the given information.

Step 5 ：Use the properties of sine and cosine functions to find the equivalent expression for $\sin 63^{circ}$.

Step 6 ：$\sin 63^{circ} \approx 0.891$ and $\sin 117^{circ} \approx 0.891$

Step 7 ：\(\boxed{\sin 63^{circ} \text{ is equal to } \sin 117^{circ}}\)