Lesson 28.2

Lesson 28.2 p. 31-35

Use cosine ratio.

Use the digits 1 to 9 at most one time each, to fill in the
blanks to create a right triangle from the vertex (2,3).

2, 3

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Multiple Choice

Use the triangle to find the

$$\sin\alpha=$$  
Be sure to reduce the answer, if needed.

• $$\frac{15}{8}$$  

• $$\frac{17}{8}$$  

• $$\frac{8}{17}$$  

• $$\frac{15}{17}$$  

Labelling

Label the parts of the special right triangle.

Drag labels to their correct position on the image

Hippopotenuse

Short Leg

Medium Leg

Hypotenuse

Long Leg

Multiple Choice

Find the measure of the missing angle.

• 90^o
• 10⁰
• 130^o
• 50^o

Multiple Choice

To use the Pythagorean Theorem, we need...

• A triangle with 2 known angles
• A right triangle with 2 known angles
• A triangle with 2 known sides
• A right triangle with 2 known sides

Multiple Choice

Find the length of the missing side. 

• 17 cm
• 22 cm
• 15 cm
• 13 cm

Multiple Select

Which of the following are considered special right triangles?

• 30-60-90

• 45-45-90

• 20-70-90

• 40-50-90

Multiple Choice

What is the ratio for Tangent?

• Adjacent Leg / Opposite Leg
• Adjacent Leg / Hypotenuse
• Opposite Leg / Hypotenuse 
• Opposite Leg / Adjacent Leg

Multiple Choice

What is the ratio for Sine?

• Opposite Leg / Adjacent Leg
• Opposite Leg /  Hypotenuse
• Adjacent Leg / Hypotenuse
• Adjacent Leg / Opposite Leg

Multiple Choice

What is the ratio for Cosine?

• Opposite Leg / Adjacent Leg
• Opposite Leg / Hypotenuse
• Adjacent Leg / Hypotenuse
• Hypotenuse / Adjacent Leg

Labelling

Label the

reference angle

hypotenuse

opposite leg

adjacent leg

Drag labels to their correct position on the image

opposite leg

cosine

adjacent leg

tangent

sine

hypotenuse

theta

cosine and
inverse cosine

Multiple Choice

Choose the correct set-up to solve for x.

• $$\sin\left(37^{\circ}\right)=\frac{x}{14}$$

• $$\cos\left(37^{\circ}\right)=\frac{x}{14}$$

• $$\tan\left(37^{\circ}\right)=\frac{x}{14}$$

• $$\sin\left(37^{\circ}\right)=\frac{14}{x}$$

Multiple Choice

What is the correct equation that can be used to solve for Angle A?

• $$\sin\left(A\right)=\frac{10}{14}$$

• $$\cos\left(A\right)=\frac{10}{14}$$

• $$\tan\left(A\right)=\frac{10}{14}$$

• $$\tan\left(A\right)=\frac{14}{10}$$

Multiple Choice

We now know  $$\cos\left(A\right)=\frac{10}{14}$$  

So we have to use inverse cosine to solve it.   Which one below is correct?

• $$A=\sin^{-1}\left(\frac{10}{14}\right)$$

• $$A=\cos^{-1}\left(\frac{10}{14}\right)$$

• $$A=\tan^{-1}\left(\frac{10}{14}\right)$$

• $$A=\tan^{-1}\left(\frac{14}{10}\right)$$

Multiple Choice

Find the measure of the indicated angle.  

• $$\sin^{-1}\left(\frac{15}{16}\right)$$

• $$\cos^{-1}\left(\frac{15}{16}\right)$$  

• $$\tan^{-1}\left(\frac{15}{16}\right)$$  

• Good question

Match

Match the following

• sine

• cosine

• tangent

• $$\sin^{-1}$$

• $$\cos^{-1}$$

• $$\frac{opposite\ leg}{hypotenuse}$$

• $$\frac{adjacent\ leg}{hypotenuse}$$

• $$\frac{opposite\ leg}{adjacent\ leg}$$

• $$\theta=\sin^{-1}\left(\frac{opposite\ leg}{hypotenuse}\right)$$

• $$\theta=\cos^{-1}\left(\frac{adjacent\ leg}{hypotenuse}\right)$$

Poll

I can write an equation with inverse trigonometry to solve for an angle.

• Yes

• I think I kind of understand but I am still confused

• No

Poll

If I were given a problem that involved trigonometry, I know if I am supposed to use regular trigonometry or inverse trigonometry to solve the problem.

• Yes, I got this!

• I would be able to if you gave me a hint

• If you talked me through every step I could do it

• Even if you showed my an example and asked me to explain what you did I still would have not clue

Poll

I know the difference between sine and inverse sine.

• Yes

• I think I kind of understand but I am still confused

• No

Find the measurement of y.

Find all missing measurements.

x

Find all missing measurements.

x

x

Find the missing measurements.

Find the missing measurements.

x

Find the missing measurements.

x

Find the missing measurements.

x

Work

p. 31-35