Trigonometry SohCahToa

SOH-CAH-TOA

Dr. Tom Giles

SOH-CAH-TOA

This does not need to apply to ONLY the special right triangles. It can apply to ANY right triangle.

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Recall:

SOHCAHTOA​

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Naming the Sides

• Hypotenuse: Across from the right angle

• Theta: Angle given or looking for

• Opposite: Side opposite of theta

• Adjacent: Side next to theta

Multiple Choice

Identify the hypotenuse

• a

• b

• c

Multiple Choice

Identify leg adjacent to <B

• a

• b

• c

Multiple Choice

Identify leg opposite <B

• a

• b

• c

Multiple Choice

Length of side opposite <X

• 21

• 29

• 20

Multiple Choice

Length of leg adjacent to <Z

• 40

• 9

• 41

Multiple Choice

Length of Hypotenuse

• 30

• 40

• 50

Try taking the ratio of these!

For example...

Multiple Choice

Ratio of:
Leg opposite <C / Leg adjacent <C

• 7/24

• 24/7

• 24/25

• 7/25

Multiple Choice

Ratio of:
Leg adjacent to <A / Hypotenuse

• 7/25

• 7/24

• 24/7

• 24/25

Multiple Choice

Ratio of:
Side opposite <A / Hypotenuse

• 7/25

• 24/25

• 7/24

• 24/7

We can use these ratios to find missing side lengths

• Calculator in degree mode

• Set up ratio- solve for side

Multiple Choice

• $$\frac{29}{21}$$  

• $$\frac{21}{20}$$  

• $$\frac{20}{29}$$  

• $$\frac{20}{21}$$  

Multiple Choice

$$Cos\left(A\right)=$$  

• $$\frac{15}{8}$$  

• $$\frac{8}{17}$$  

• $$\frac{8}{15}$$  

• $$\frac{17}{8}$$  

Multiple Choice

Determine the  $$\sin\left(\theta\right)$$  given the diagram:

• $$\frac{6}{5}$$  

• $$\frac{5}{6}$$  

Multiple Choice

Q4: Given triangle XYZ, find $$\tan\left(\angle Y\right)$$  if XY=50, YZ=40, and XZ=30

• $$\frac{30}{40}$$  

• $$\frac{40}{50}$$  

• $$\frac{50}{30}$$  

• $$\frac{40}{30}$$  

Multiple Choice

 Find tanZ

• 35/21

• 21/28

• 35/28

• 28/21

Multiple Choice

 Find cosC

• 16/34

• 16/30

• 30/34

• 34/16

Multiple Choice

 Find sinA

• 32/40

• 32/24

• 24/40

• 24/32

Multiple Choice

 Find sinA

• 32/40

• 32/24

• 24/40

• 24/32

Multiple Choice

Find cosA

• 30/16

• 30/34

• 30/15

• 16/34

Multiple Choice

Find cosA

• 30/16

• 30/34

• 30/15

• 16/34