Master Trigonometry Applications: Enhance Your Nursing Practice

Question 1

A ladder is leaning against a wall. The base of the ladder is 3 meters from the wall, and the top of the ladder is 5 meters high. What is the angle of elevation of the ladder?

Accepted Answer

37 degrees

Answer

30 degrees

Answer

45 degrees

Answer

60 degrees

Question 2

A triangle has angles of 45 degrees and 60 degrees. The side opposite the 45-degree angle is 10 units long. What is the length of the side opposite the 60-degree angle?

Accepted Answer

5√2 units

Answer

10√2 units

Answer

10 units

Answer

5 units

Question 3

A physical therapist is using trigonometry to determine the angle of a patient's knee flexion. The patient is lying down and the physical therapist measures the horizontal distance from the patient's knee to the ground as 20 centimeters and the vertical distance from the patient's knee to the top of their thigh as 15 centimeters. Calculate the angle of knee flexion.

Accepted Answer

36.9 degrees

Answer

73.8 degrees

Answer

26.2 degrees

Answer

53.1 degrees

Question 4

A nurse is measuring the circumference of a patient's wound. The circumference is 15 cm. What is the radius of the wound in centimeters?

Accepted Answer

2.39 cm

Answer

3.59 cm

Answer

1.19 cm

Answer

4.78 cm

Question 5

A patient is lying in bed with their head elevated 30 degrees. The length of the patient's body (from head to toe) is 72 inches. As a nurse, you need to calculate the height of the patient's head (in inches) above the horizontal plane.

Accepted Answer

22.63

Answer

18.00

Answer

14.39

Answer

28.00

Question 6

A nurse is measuring the angle of a patient's hip flexion. The nurse measures the length of the patient's thigh from the hip to the knee as 15 inches and the length of the patient's leg from the knee to the ankle as 10 inches. Calculate the angle of hip flexion.

Accepted Answer

32.49°

Answer

45.00°

Answer

90.00°

Answer

57.51°

Question 7

A nurse is measuring the circumference of a patient's head. The circumference is 56 centimeters. What is the diameter of the patient's head?

Accepted Answer

17.78 cm

Answer

28 cm

Answer

56 cm

Answer

35.56 cm

Question 8

A nurse is measuring the angle of a patient's knee joint. The angle is measured to be 120 degrees. What is the measure of the complementary angle?

Accepted Answer

60 degrees

Answer

150 degrees

Answer

30 degrees

Answer

90 degrees

Question 9

A nurse is using a syringe to inject medication into a patient's arm. The needle is inserted at a 15-degree angle to the skin. If the needle is 2 inches long, how deep will it penetrate the skin?

Accepted Answer

1.93 inches

Answer

1.5 inches

Answer

2.5 inches

Answer

2 inches

Question 10

A patient is lying on their side with their leg elevated at a 45-degree angle. If their leg is 20 inches long, how high is their knee from the bed?

Accepted Answer

14.14 inches

Answer

10 inches

Answer

5 inches

Answer

20 inches

Question 11

A patient is sitting in a chair with their arm extended out to the side. Their arm is 25 inches long and makes a 30-degree angle with the horizontal. How far is the patient's hand from their shoulder?

Accepted Answer

21.65 inches

Answer

25 inches

Answer

12.5 inches

Answer

30 inches

Question 12

A nurse is using a suction machine to clear a patient's airway. The suction tube is 18 inches long and makes a 45-degree angle with the patient's mouth. How deep into the patient's airway will the suction tube reach?

Accepted Answer

12.73 inches

Answer

18 inches

Answer

6 inches

Answer

9 inches

Question 13

Which of the following is an application of trigonometry in nursing?

Accepted Answer

Calculating angles of insertion for IVs

Answer

Drug dosage calculations

Answer

Positioning patients for surgery

Answer

Determining distances in complex shapes

Question 14

What is the value of sin(60 degrees)?

Accepted Answer

sqrt(3) / 2

Answer

sqrt(2) / 2

Answer

1 / 2

Answer

1

Question 15

What is the value of cos(30 degrees)?

Accepted Answer

sqrt(3) / 2

Answer

1 / 2

Answer

sqrt(2) / 2

Answer

1

Question 16

A nurse needs to measure the height of a patient's intravenous (IV) bag hanging above the bed. The bag is 3 feet above the floor and the IV line makes a 25-degree angle with the horizontal. How high is the IV bag above the bed if the bed is 3 feet tall?

Accepted Answer

3.58 feet

Answer

3.8 feet

Answer

5.2 feet

Answer

2.7 feet

Question 17

A nurse is administering medication to a patient. The medication bottle indicates a dosage of 10 ml. The nurse uses a syringe with a 20 ml capacity. What is the angle of the syringe's plunger if the nurse has drawn 5 ml of medication?

Accepted Answer

30 degrees

Answer

45 degrees

Answer

60 degrees

Answer

15 degrees

Question 18

A patient is recovering from surgery and needs to be repositioned every 2 hours. The nurse uses a mechanical lift to move the patient. The lift arm extends 5 feet and makes a 30-degree angle with the horizontal. What is the vertical distance the lift arm raises the patient?

Accepted Answer

2.5 feet

Answer

1.5 feet

Answer

4.3 feet

Answer

3.5 feet

Question 19

A nurse is monitoring a patient's vital signs. The patient's temperature is 102 degrees Fahrenheit. The nurse needs to convert this temperature to Celsius. Using the formula C = (F - 32) * 5/9, what is the patient's temperature in Celsius?

Accepted Answer

38.9 degrees Celsius

Answer

32.2 degrees Celsius

Answer

41.1 degrees Celsius

Answer

35.6 degrees Celsius

Question 20

A nurse is administering an intravenous drip to a patient. The drip rate is set at 100 ml/hour. How many milliliters will the patient receive in 30 minutes?

Accepted Answer

50 ml

Answer

25 ml

Answer

100 ml

Answer

75 ml

Question 21

A nurse needs to administer a medication that requires a specific dose per kilogram of body weight. The patient weighs 150 pounds. The nurse needs to convert the patient's weight to kilograms to calculate the correct dosage. What is the patient's weight in kilograms?

Accepted Answer

68 kg

Answer

45 kg

Answer

54 kg

Answer

78 kg

Question 22

A nurse is caring for a patient with a urinary tract infection (UTI). The doctor has prescribed a 1000 ml intravenous fluid bolus over 4 hours. What is the flow rate in milliliters per minute?

Accepted Answer

41.7 ml/min

Answer

25 ml/min

Answer

33.3 ml/min

Answer

50 ml/min

Question 23

A nurse is assessing a patient's blood pressure. The systolic pressure is 120 mmHg and the diastolic pressure is 80 mmHg. What is the patient's pulse pressure?

Accepted Answer

40 mmHg

Answer

60 mmHg

Answer

100 mmHg

Answer

20 mmHg

Question 24

A nurse is calculating the dosage of medication for a child. The child's weight is 25 kg. The doctor has prescribed 5 mg/kg of medication. What is the total dosage the child should receive?

Accepted Answer

125 mg

Answer

50 mg

Answer

150 mg

Answer

100 mg

Question 25

A nurse is preparing a medication for a patient. The medication bottle indicates a concentration of 500 mg/5 ml. The nurse needs to administer a 200 mg dose. How many milliliters of medication should the nurse administer?

Accepted Answer

2 ml

Answer

3 ml

Answer

1 ml

Answer

4 ml

Question 26

A nurse needs to calculate the angle of elevation of a patient's IV drip bag. The bag is hanging 2 feet above the patient's arm, and the drip line is 3 feet long. What is the angle of elevation?

Accepted Answer

41.8 degrees

Answer

53.1 degrees

Answer

26.6 degrees

Answer

60 degrees

Question 27

A nurse needs to measure the length of a wound on a patient's leg. The wound is 1 inch wide and 2 inches long. Using the Pythagorean theorem, what is the approximate length of the diagonal of the wound?

Accepted Answer

2.24 inches

Answer

3 inches

Answer

4 inches

Answer

1.41 inches

Question 28

A patient needs to be moved from their bed to a wheelchair. The distance between the bed and the wheelchair is 5 feet, and the height difference between the bed and the wheelchair is 1 foot. What is the angle of inclination of the ramp that needs to be used to move the patient safely?

Accepted Answer

11.3 degrees

Answer

30 degrees

Answer

45 degrees

Answer

21.8 degrees

Question 29

A nurse is administering medication using a syringe. The syringe is filled to a level of 2 ml, and the needle is 1 inch long. What is the angle of the needle relative to the syringe if the needle is inserted at a depth of 0.5 inches?

Accepted Answer

30 degrees

Answer

45 degrees

Answer

60 degrees

Answer

90 degrees

Question 30

A nurse needs to measure the circumference of a patient's arm to determine the appropriate size of a blood pressure cuff. The patient's arm has a diameter of 10 cm. What is the circumference of the arm?

Accepted Answer

31.4 cm

Answer

100 cm

Answer

15.7 cm

Answer

62.8 cm

Question 31

A patient is receiving intravenous fluids. The IV bag is hanging 1.5 meters above the patient's vein, and the drip line is 2 meters long. What is the angle of depression of the drip line relative to the horizontal?

Accepted Answer

48.6 degrees

Answer

36.9 degrees

Answer

60 degrees

Answer

53.1 degrees

Question 32

A nurse needs to administer an intramuscular injection at a 90-degree angle. The needle is 1 inch long, and the nurse wants to inject the medication 1.5 inches deep. How far away from the patient's skin should the nurse insert the needle?

Accepted Answer

0.5 inches

Answer

1 inch

Answer

2 inches

Answer

1.5 inches

Question 33

A nurse is using a graduated cylinder to measure medication. The cylinder is filled to a level of 50 ml, and the diameter of the cylinder is 4 cm. What is the height of the medication in the cylinder?

Accepted Answer

3.98 cm

Answer

7.96 cm

Answer

1.99 cm

Question 34

A patient's bed needs to be raised to a specific angle for comfort. The bed is 2 feet long, and the head of the bed needs to be raised by 6 inches. What is the angle of elevation of the bed?

Accepted Answer

8.53 degrees

Answer

25.58 degrees

Answer

17.05 degrees

Question 35

A nurse is using a sling to support a patient's injured arm. The sling is attached to the patient's shoulder at an angle of 30 degrees to the horizontal. If the sling is 20 inches long, how far below the patient's shoulder is the arm supported?

Accepted Answer

10 inches

Answer

11.55 inches

Answer

17.32 inches

Answer

20 inches