Trigonometry Sohcahtoa

Learning Sohcahtoa

Multiple Choice

What is the length of the hypotenuse in this triangle?

• 124

• 141

• 188

• There is no hypotenuse

Multiple Choice

With regard to the reference angle shown, which side is the OPPOSITE side?

• x

• y

• w

Multiple Choice

With regard to  $$\theta$$  which side is the adjacent in this RAT?

• q

• m

• p

Multiple Choice

If  $$56^{\circ}$$  is the reference angle, which is the adjacent side?

• u

• g

• k

Multiple Choice

If  $$34\degree$$ is the reference angle, which is the adjacent side?   

• u

• g

• k

Multiple Choice

Which is the hypotenuse in this triangle?

• c

• a

• b

• There is no hypotenuse

Multiple Choice

With   $$64\degree$$   as the reference angle, which is the opposite side?

• AB

• BC

• AC

Multiple Choice

What is the value of the unknown angle at the corner labelled B?

• $$26\degree$$

• $$36\degree$$

• $$64\degree$$

• $$90\degree$$

The trigonometric ratios

There are three trigonometric ratios. They are ONLY used with Right Angled Triangles (RATs)

Sine ratio

The sine ratio is abbreviated as sin
For a given reference angle, the sine ratio is the ratio

 $\frac{\text{opposite}}{\text{hypotenuse}}$  

Cosine ratio

The cosine ratio is abbreviated as cos. For a given reference angle, the cosine ratio is:

 $\frac{\text{adjacent}}{\text{hypotenuse}}$  

 Tangent ratio

The tangent ratio is abbreviated as tan. For a given reference angle, the tangent ratio is:

 $\frac{\text{opposite}}{\text{adjacent}}$  

label triangle first!

(i) Sine

 $\sin\left(\beta\right)=\frac{\text{opp}}{\text{hyp}}$  

Solution

Start with the sine ratio.

 $\sin\left(\beta\right)=\frac{\text{opp}}{\text{hyp}}$  

 $\sin\left(\beta\right)=\frac{\text{}b}{c}$  

Multiple Choice

What is an expression for 
$$\cos\left(\beta\right)$$  ?

• $$\frac{c}{a}$$  

• $$\frac{a}{c}$$  

• $$\frac{b}{c}$$  

• $$\frac{c}{b}$$  

• $$\frac{a}{b}$$  

Multiple Choice

What is an expression for
$$\tan\left(\beta\right)$$  ?

• $$\frac{a}{c}$$  

• $$\frac{b}{c}$$  

• $$\frac{b}{a}$$  

• $$\frac{a}{b}$$  

• $$\frac{c}{a}$$  

Multiple Choice

What is a correct trigonometric ratio for the triangle shown?

• $$\tan\left(\gamma\right)=\frac{a}{c}$$

• $$\sin\left(\gamma\right)=\frac{c}{a}$$

• $$\cos\left(\gamma\right)=\frac{c}{b}$$

• $$\sin\left(\gamma\right)=\frac{c}{b}$$

Multiple Choice

Which equation would be correct for the right angled triangle shown?

• $$\tan\left(35\degree\right)=\frac{t}{17}$$

• $$\sin\left(35\degree\right)=\frac{t}{17}$$

• $$\cos\left(35\degree\right)=\frac{17}{t}$$

• $$\sin\left(35\degree\right)=\frac{17}{t}$$

Multiple Choice

Which equation would be true for the triangle shown?

• $$\tan\left(\theta\right)=\frac{20}{31}$$

• $$\sin\left(\theta\right)=\frac{20}{31}$$

• $$\cos\left(\theta\right)=\frac{20}{31}$$

• $$\tan\left(\theta\right)=\frac{31}{20}$$

• $$\sin\left(\theta\right)=\frac{31}{21}$$