Trigonometry

Question 1

What is the longest side of a triangle?

Answer 1

The hypotenuse

Question 2

What is the name of the side that directly faces the given angle?

Answer 2

The opposite

Question 3

What is the name of the side that runs from the given angle to the right side?

Answer 3

The adjacent

Question 4

What is the method for remembering Sin , Cos and Tan?

Answer 4

Sin α = Sine is Opposite over Hypotenuse, Cos α = Cosine is Adjacent over Hypotenuse and Tan α = Tangent is Opposite over Adjacent

Question 5

A triangle has an opposite side of 80 metres and an angle of 55 degrees. Find the side of the hypotenuse correct to two decimal places.

Answer 5

x = 80/sin(55°)
x = 97.66m

Question 6

A triangle has an opposite side of 66 centimetres and an angle of 37 degrees. Find the side of the hypotenuse correct to one decimal place.

Answer 6

x = 66/sin(66°)
x = 72.2cm

Question 7

A triangle has an adjacent side of 57 kilometres and an angle of 44 degrees. Find the side of the hypotenuse correct to three decimal places.

Answer 7

x = 57/cos(44°)
x = 79.239km

Question 8

A triangle has an adjacent side of 108 metres and an angle of 71 degrees. Find the side of the hypotenuse correct to one decimal place.

Answer 8

x = 108/cos(71°)
x = 331.7m

Question 9

A triangle has an adjacent side of 22 metres and an angle of 11 degrees. Find the side of the opposite correct to one decimal place.

Answer 9

x = 22/tan(11°)
x = 113

Question 10

What does °, ‘ and “ equate to in time?

Answer 10

° = hours
' = minutes
" = seconds

Question 11

Convert 3 hours, 27 minutes and 45 seconds to degrees.

Answer 11

3h, 27m, 45s = 3° 27’ 45” = 3° 28’

Question 12

Convert 6 hours, 16 minutes and 20 seconds to degrees.

Answer 12

6h, 16m, 20s = 6° 16’ 20” = 6° 16’

Question 13

How do you convert degrees to time on a calculator?

Answer 13

Press the ° ‘ ‘’ button on a calculator.

Question 14

How do you find the unknown side of a right angled triangle? List the 3 steps.

Answer 14

1. Identify the two labelled sides and decide whether to use sin, cos or tan.
2. Write an equation using the ratio, the angle variable and the two sides as a fraction.
3. Solve the equation to find the value of the variable.

Question 15

How do you find the unknown angle of a right angled triangle? List the 3 steps.

Answer 15

1. Identify the two known sides and decide whether to use sin, cos and tan.
2. Write an equation using the ratio, the angle variable and the two sides as a fraction.
3. Use the calculator’s inverse trigonometric function to find the size of the angle.