Please help me with these five math Qs. 10 points?

Question

19: In triangle PQR, P = 35°, Q = 23°, QR = 9.4. Find RP.

9.4

6.4

40.96

41.96

20: In the same triangle as #19, find PQ.

3.99

-13.89

13.89

72.64

21: In oblique triangle ABC, C = 105°, a = 21.3, and b = 32.0. Find c.

42.78

1.50

1830.13

105

22: The sides of a parallelogram are AB = 209.16 and AD = 347.25, and the diagonal AC = 351.47. Find the length of the other diagonal.

432.67

452.92

109.54

107.32

23: Suppose you have a vector of magnitude 18 and another vector of magnitude 12, with 36° between the two. What is the magnitude of their resultant?

4.01

108.37

16.32

28.59

24: The airspeed of a small plane is 200 km/h. The wind speed is 50.0 km/h from the West (remember, that means it’s blowing to the East). Determine the velocity of the plane relative to the ground if the pilot keeps the plane pointing North.

207 km/h

206 km/h

109 km/h

32 km/h

25: A swimmer on the south shore of a river wishes to swim to a dock directly north of her starting point. Her maximum swimming speed in still water is 4.0 km/h and there is a current in the river flowing 2.5 km/h towards the west. How many degrees to the East must she swim so that she goes straight north across the river?

18.22°

16.34°

38.68°

87.68°

Answer 1

There are 7 Qs, please limit one per question. I will do only 19 - 23 since you did say 5 Qs, unfortunately I cannot be very descriptive because you offered too many questions.

19.) Law of sines

94 / Sin 35° = PR / Sin 23°

PR = 25

20.) Triangle sum & Law of sines

180 - 35 - 23 = 122°

94 / Sin 35° = PR / Sin 122°

PR = 54.3

21.) Law of cosines

c^2 = 21.3 ^2 + 32 ^2 - 2(21.3)(32)(cos 105°)

c^2 = 1830.5

c = 42.7

22.) AD = BC = 347.25, find B, use certain properties of parallelograms to find A, use law of cosines.

351^2 = 209.16^2 + 347.25 ^2 - 2(209.16)(347.25)(cos B)

.283141 = cos B

B = 73.55°

23.)