Trigonometric Ratios

Trigonometric Ratios

Remember, each of these ratios relies on you identifying the sides of the triangle based on your reference angle.

Name Sides in Right-Angled Triangles

• The Hypotenuse

• The opposite side

• The adjacent side

Multiple Choice

What is the length of the hypotenuse?

• 16

• 30

• 34

Multiple Choice

What is the length of the side opposite ∠X?

• 16

• 30

• 34

Multiple Choice

What is the length of the side adjacent to ∠Z?

• 16

• 30

• 34

Multiple Choice

The side adjacent to angle

$$\theta$$  is ...

• LM

• LN

• MN

Multiple Choice

The hypotenuse is ...

• LM

• LN

• MN

Multiple Choice

The side opposite to angle

$$\theta$$  is ...

• LM

• LN

• MN

Multiple Choice

What is the name given to the longest side of a right-angled triangle?

• Hypotenuse

• Opposite

• Adjacent

Multiple Choice

The side ‘next to’ the marked angle is called:

• Hypotenuse

• Touching

• Adjective

• Adjacent

Multiple Choice

What is the opposite angle to the side with length 12 m?

• angle A

• angle B

• angle C

Multiple Choice

Which angle must be the right angle for this triangle?

• angle A

• angle B

• angle C

Complementary Angles

• The three angles in any triangle add to 180°.

• Since one angle in a right-angled triangle measures 90°, the other two angles must add to 90° to make up the 180°.

• The two acute angles in any right-angled triangle are complementary angles (ie add to 90°).

Multiple Choice

Complementary angles add together to give:

• $$90\degree$$

• $$180\degree$$

• $$360\degree$$

Multiple Choice

What is the size of angle P?

• $$90\degree$$

• $$24\degree$$

• $$66\degree$$

• $$76\degree$$

Multiple Choice

What is the size of the missing angle in this triangle?

• $$20\degree$$

• $$30\degree$$

• $$90\degree$$

• $$160\degree$$

Multiple Choice

What is the complement of 50⁰?

• $$90\degree$$

• $$50\degree$$

• $$40\degree$$

• $$30\degree$$

Multiple Choice

In which of these diagrams are all sides correctly named, with respect to angle P?

Fill the highlighted information into your Math Notebook. Copy all if writing on regular paper.

Fill the highlighted information into your Math Notebook. Copy all if writing on regular paper.

Multiple Choice

What is the ratio for Sine?

• Hyp/Opp

• Opp/Hyp

• Opp/Adj

• Adj/Opp

Multiple Choice

What is the ratio for Tangent

• Opp/Adj

• Adj/Opp

• Opp/Hyp

• Hyp/Opp

Multiple Choice

What is the opposite side to <D?

• EF

• DF

• DE

Multiple Choice

What is the ratio for Cosine?

• Opp/Hyp

• Opp/Adj

• Adj/Opp

• Adj/Hyp

Multiple Choice

What is the length of the opposite side?

• 8

• 15

• 17

Multiple Choice

What is the length of the adjacent side?

• 8

• 15

• 17

Multiple Choice

What is the length of the hypotenuse side?

• 8

• 15

• 17

Multiple Choice

Find $$\tan51\degree$$

• 1.2349

• .9030

• .9

• 1.23

Multiple Choice

Find $$\cos87\degree$$

• .05

• .569

• .0523

• .5700

Multiple Choice

Which one is the easy way to remember trigonometric ratios?

• Sah Coh Toa

• Soh Cah Toa

• Soh Cah Tao

• Soh Ceh Toa

Multiple Choice

What is the ration for

$$\sin\ \left(\theta\right)$$  ? 

• $$\frac{8}{15}$$  

• $$\frac{15}{17}$$  

• $$\frac{8}{17}$$  

Multiple Choice

What is the ration for

$$\cos\ \left(\theta\right)$$  ? 

• $$\frac{8}{15}$$  

• $$\frac{15}{17}$$  

• $$\frac{8}{17}$$  

Multiple Choice

What is the ratio for

$$\tan\ \left(\theta\right)$$  ? 

• $$\frac{8}{15}$$  

• $$\frac{15}{17}$$  

• $$\frac{8}{17}$$  

Multiple Choice

Which ratio is the Sine of Angle C?

• ²⁴/₃₀

• ¹⁸/₃₀

• ³⁰/₂₄

• ³⁰/₁₈

Multiple Choice

What is the ratio of Sine of Angle Z?

Sin Z =?

• 24/32

• 32/24

• 32/40

• 24/40

Multiple Choice

What is ratio of Sin A?

• 32/40

• 32/24

• 24/40

• 24/32

Multiple Select

 Which triangle below shows the ratio as $$\sin\left(x\right)=\frac{b}{c}$$  ?

Multiple Choice

What is the ratio of Cosine of Angle C?

• 9/41

• 9/40

• 40/41

• 40/9

Multiple Choice

Find the ratio of cos B.

• 3/5

• 3/4

• 4/5

• 5/4

Multiple Choice

What is the reduced ratio for cos X?

• 15/36 = 5/12

• 15/39 = 5/13

• 36/39 = 2/13

• 36/15 = 12/5

Multiple Choice

Find the ratio of Cos Z.

• 18/30 = 3/5

• 18/24 = 3/4

• 24/30 = 4/5

• 24/18 = 4/3

Multiple Select

 Which triangle below shows the ratio of $$\cos\ \left(x\right)=\frac{a}{b}$$  ?

Multiple Choice

What is the ratio of Tangent of Angle A?

• 16/20

• 20/16

• 12/16

• 16/12

Multiple Choice

Find the ration of Tan of X.

• 50/40

• 40/30

• 40/50

• 30/40

Multiple Choice

Which triangle below shows the ratio as $$\tan\ \left(x\right)=\frac{t}{u}$$  ?