Trigonometry

Question 1

Set 1 Problem 41: Convert 135° to grads.

Answer 1

150 grads

Question 2

Set 1 Problem 30: Given a triangular lot ABC with the following data on Table 1.1. What is the measure of distance BC?

Answer 2

234.76 m (p.11)

Question 3

Set 2 Problem 41: Given a triangular lot ABC with the following data on Table 1.1. What is the bearing of side CA?

Answer 3

N 58.92° W (p.29)

Question 4

Set 2 Problem 73: Two posts, one 8 ft high and the other 12 ft high, stand 15 ft apart. They are to be stayed by wires attached to a single stake on the ground level, the wires running to the tops of the posts. Where should it be staked, to use the least amount of wire?

Answer 4

6 ft from the shorter post (p.36)

Question 5

Ship A left a port at 12:00 noon and sails N 42°18’ E at a rate of 3 mph. At 2:00 PM, ship B starts from the same port and goes S 44°28’ E at a rate of 4 mph. Compute the following.
Set 3 Problem 20: The distance between the ships at 5:00 PM.

Answer 5

19.73 mi (p.44)

Question 6

Ship A left a port at 12:00 noon and sails N 42°18’ E at a rate of 3 mph. At 2:00 PM, ship B starts from the same port and goes S 44°28’ E at a rate of 4 mph. Compute the following.
Set 3 Problem 21: The bearing of B from A at 5:00 PM.

Answer 6

S 4°55’ W (p.44)

Question 7

Set 3 Problem 29: Solve the triangle with the given parts: a=8 cm, b=10 cm, c=18 cm. Which of the following is true?
A=90°
B=60°
C=194°
impossible triangle

Answer 7

impossible triangle (p.46)

Question 8

Set 4 Problem 14: Building A and B are standing vertically on the same horizontal plane. From the top of A, the angle of elevation of the top of B is 46 degrees. From the foot of B, the angle of elevation of the top of A is 28 degrees. Building B is 240 m high. Find the horizontal distance between A and B.

Answer 8

153.13 m (p.61)

Question 9

Set 4 Problem 71: Given that cosA=3s. Find the tangent of A.

Answer 9

Equation 4.1 (p.71)

Question 10

Set 4 Problem 72: There exists a value of x such that the tangent of the expression (2x+18) is equal to the cotangent of the expression (4x-12). The value of x could be

Answer 10

14° (p.71)

Question 11

Set 4 Problem 73: A tower is standing on a horizontal ground. To calculate the height of the tower, a surveyor at A, due east of the tower, measures the angle of elevation of the top of the tower and found it to be 28.4°. He then moves to point B, directly south of A, and measures the angle of elevation of the top of the tower and found it to be 23.6°. Point B is 72.8 m from A. Calculate the height of the tower.

Answer 11

53.94 m (p.71)

Question 12

Set 5 Problem 62: If sin(x-30°)=cos(y+20°), then what is x+y?

Answer 12

x+y=100° (p.86)

Question 13

Set 2 Problem 74: Given a triangular lot ABC with the following data on Table 1.1. Find the area of the lot in hectares.

Answer 13

2.48 hectares (p.89)

Question 14

Set 6 Problem 7: A triangle ABC has sides AB=12cm, BC=14cm, and AC=18cm. What is the length of the angle bisector of the angle A measured from vertex A to the terminal point on side BC?

Answer 14

13cm (p.95)

Question 15

Set 6 Problem 54: A surveyor wants to measure the width of the river. He established a line MNP, where MN represents the width of the river and point P is at a distance of 198 m from N. He also established lines NQ=312.38 m and PR=454.82 m both NQ and PR are perpendicular to MNP. Point Q is on line MR. Approximate the width of the river.

Answer 15

434.23 m (p.102)

Question 16

Set 6 Problem 55: An airplane has an airspeed (in still air) of 240 mph with the bearing S 30° W. If a wind is blowing due west at 40 mph, find the final bearing of the plane.

Answer 16

S 38° W (p.102)

Question 17

Set 7 Problem 7: A triangle has sides 12 cm, 18 cm, and 16 cm. Find the length of the median to the longest side.

Answer 17

10.91 cm (p.112)

Question 18

Set 7 Problem 38: Find an angle whose supplement exceeds 5 times its complement by 20°.

Answer 18

72.5° (p.117)

Question 19

Set 7 Problem 64: Find the equation of the line in normal form with normal intercept ρ=3, and normal angle θ=45°.

Answer 19

x+y=3sqrt(2) (p.121)

Question 20

Set 8 Problem 58: Two radio towers are standing on a level ground. The first is 132 ft tall. From a point part way up the second, it is observed that the angle of elevation of the top of the first tower is 55 degrees while the angle of depression of its base is 33 degrees. How far apart are the towers?

Answer 20

63.50 ft (p.137)

Question 21

Set 9 Problem 2: Solve the triangle with the given parts: A=42deg, a=6cm, c=12cm. Which of the following is true?
b=18cm
C=56deg
B=112.72deg
impossible triangle

Answer 21

impossible triangle (p.145)

Question 22

Set 9 Problem 38: The altitude to the hypotenuse of a right triangle divides the hypotenuse into 2 segments of lengths 6 cm and 8 cm. Find the area of the triangle.

Answer 22

48.51 m^2 (p.151)

Question 23

Set 9 Problem 50: Two interior angles of a triangle are 64° and 32°. The perimeter of the triangle is 68 m. Compute the shortest side of the triangle.

Answer 23

22.18 m (p.153)

Question 24

Set 10 Problem 32: Convert the Cartesian plane equation y=x into its equivalent spherical coordinate equation.

Answer 24

theta=pi/4 (p.167)

Question 25

Set 10 Problem 73: If the arcsin of (x-2y) is 0.5236 and arccos of (3x-4y) is 3.1416, find the value of x.

Answer 25

-2 (p.174)

Question 26

Set 10 Problem 74: A tower stands vertically on a hillside which makes an angle of 22 degrees with the horizontal. From a point 60 ft up the hill from the foot of the tower, the angle of elevation of the top of the tower is 35 degrees. How high is the tower?

Answer 26

61.43 ft (p.174)