Right Triangle Trigonometry: Missing Sides and Angles

Right Triangle Trigonometry

GOAL: To apply what we know about trigonometry to degree applications.

Multiple Choice

If I know the lengths of TWO sides of a RIGHT triangle then I can find the length of the third side.

• TRUE; using Pythagorean Theorem

• False; you would need information on an angle or two.

Multiple Choice

Find the length of the missing side. 

• 17 cm
• 22 cm
• 15 cm
• 13 cm

Multiple Choice

Find the length of the missing side. 

• 20 in.
• 68 in.
• 16 in.
• 80 in.

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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Multiple Select

Focus in on the 70^o angle...which two sides are "identified" in the figure?

• opposite

  (an unknown)

• hypotenuse

  (4 units)

• adjacent

  (no marking)

• None of these

Multiple Choice

So we should have found;

opposite side = ?

hypotenuse = 4

(remember...related to the 70^o angle!!!) Which trig ratio uses these two sides?

• sine (sin)

• cosine (cos)

• tangent (tan)

• None of these

​sin70^o = ?/4

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Check to be sure your calculator is in DEGREE MODE.

If you need help here - ask Mr Delgado​

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​So - consider this;

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sin70^o is about 0.9396926...

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0.9396926...=?/4​

How do you solve for the ?​

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Multiple Choice

$$0.9396926...=\frac{?}{4}$$  , to solve

• multiply both sides by 4

• divide both sides by 4

• add 4 to both sides

• subtract 4 from both sides

Multiple Choice

Since we need to multiply both sides by 4 given $$0.9396926...=\frac{?}{4}$$  , the length of the side marked with a ? is __.

• 3.7588

  $$4\cdot\sin70\degree$$  

• 3.6

  $$.9\cdot4$$  

• 0.2349

  $$\frac{\sin70}{4}$$  

• -0.9848

  $$\sin70\cdot4$$  

Multiple Select

Let's consider angle B (25^o). Which two sides do "b" and "8" represent?

• Opposite

• Adjacent

• Hyptonuse

• All of them

Multiple Choice

Let's focus on these two;

Opposite Side = "b"

Adjacent Side = "8"

(in relationship to angle B)

Which trig ratio uses these two sides?

• sine (sin)

• cosine (cos)

• tangent (tan)

• none of them

Multiple Choice

So now...which of the following equations would hold true?

• $$\tan\left(25\degree\right)=\frac{b}{8}$$  

• $$\tan\left(8\degree\right)=\frac{25}{b}$$  

• $$\tan\left(25\degree\right)=\frac{8}{b}$$  

• $$\tan\left(b\degree\right)=\frac{8}{25}$$  

Multiple Choice

Which of the following best represents the length of side "b?"

• 3.73

• 177.88

• 17.16

• 17.74

Multiple Choice

Choose the correct set up to find the length of the side x.

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

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

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

• None of these are correct

Multiple Choice

Find the value of x.

• 8.43

• 11.18

• 10.55 

• None of these are correct

Multiple Choice

What is the correct set up for the problem to solve for side w?

• $$\sin\left(40\degree\right)=\frac{w}{28}$$  

• $$\cos\left(40\degree\right)=\frac{w}{28}$$  

• $$\tan\left(40\degree\right)=\frac{w}{28}$$  

• $$\sin\left(40\degree\right)=\frac{28}{w}$$  

Multiple Choice

What is the length of side "w?"

• 18.0 

• 21.4

• 23.5

• 43.56 

Multiple Choice

OK, go...Find the length of "x."

• 6.57 cm
• 7 cm
• 7.44 cm
• 26.33 cm