In the ∆OPQ, right-angled at P, PQ = 5cm, and OQ - OP = 3cm. Determine the value of sin Q + cos Q.

A) \$ 24/17\$

B) \$ 41/40\$

C) \$ 33/17\$

D) \$ 23/17\$

In the given figure, BC: AC = 3 : 4 and perimeter of △ABC = 60 cm. Determine AC, CD, and BA.

A) AC = 20 cm , CD = 30 cm and BA = 25 cm

B) AC = 25 cm , CD = 30 cm and BA = 20 cm

C) AC = 30 cm , CD = 20 cm and BA = 25 cm

D) AC = 20 cm , CD = 25 cm and BA = 30 cm

If in a right-angled triangle ABC, right-angled at B, hypotenuse AC = 4cm, base BC = 7cm, and perpendicular AB = 3cm and if ∠ACB = \$ \theta\$, then find tan \$ \theta\$, sin \$ \theta\$, and cos \$ \theta\$.

A) \$tan \theta = 3/7, sin \theta = 4/3, cos \theta = 7/4\$

B) \$tan \theta = 3/7, sin \theta = 3/4, cos \theta = 4/7\$

C) \$tan \theta = 3/7, sin \theta = 3/4, cos \theta = 7/4\$

D) \$tan \theta = 7/3, sin \theta = 4/3, cos \theta = 7/4\$

In a right triangle ABC, right-angled at B, If tan A = 1 then find the value 2sinAcosA.

A) 2

B) 1

C) -1

D) -2

In a triangle XYZ, right-angled at Y, XY = 15 inches, and angle \$ X = 30^o\$.Find cos X.

A) \$ 1/2\$

B) -2

C) \$- 1/2\$

D) 2