using right triangle trigonometry (trig, for short!)

Using Right TriangleTrigonometry(trig, for short!)

MathScience Innovation Center

Betsey Davis

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis

Geometry SOL 7 The student will solve practical

problems using: Pythagorean Theorem Properties of Special Triangles Right Triangle Trigonometry


Practical Problem Example 1 Jenny lives 2 blocks down and 5

blocks over from Roger. How far will Jenny need to walk if

she takes the short cut?

J

R Pythagorean Theorem2^2 +5 ^2 = ?

29

So shortcut is blocksaboutor 4.529


Practical Problem Example 2 Shawna wants to build a triangular deck

to fit in the back corner of her house. How many feet of railing will she need

across the opening?

Special 30-60-90 triangle

Hypotenuse is 10 feet

She will need 10 feet of railing

feet35

5 feetRailing across

here


Practical Problem Example 3 Rianna wants to find the angle

between her closet and bed.

We don’t need the pythagorean theorem

It is not a special triangle

We don’t need trig

We just need to know the 3 angles add up to 180

X is 50

100ox

30o


Review Find: Sin A Cos A Tan A

5

12

13

A

= 5/13

= 12/13

= 5/12

S = O/H C = A/H T = O/A


If you know the angles,the calculator gives you sin, cos, or tan: Check MODE to be sure DEGREE is

highlighted (not radian) Press SIN 30 ENTER Press COS 30 ENTER Press TAN 30 ENTER

Write down your 3 answers


What answers did you get? Sin 30 = .5 Cos 30 = .866 Tan 30 = .577

These ratios are the ratios of the legs and hypotenuse in the right triangle.

8

30

60?

?

4

93.634 aboutor

Sin 30 = O/H = 4/8=.5

cos 30 = A/H = 6.93/8=.866tan 30 = O/A = 4/6.93=.577


If sin, cos, tan can be found on the calculator, we can use them to find missing triangle sides.

20o

50?

?


If sin, cos, tan can be found on the calculator, we can use them to find missing triangle sides.

20o

50x

y

Sin 20 = x /50

Cos 20 = y/50

Tan 20 = x /y


Let’s solve for x and y

20o

50x

y

Sin 20 = x /50

cos 20 = y/50

.342 = x/50

17.1 = x

.940 = y/50

47 = y


Do the answers seem reasonable?

20o

5017.1

47

No, but the diagram is not reasonable either.


Practical Problem Example 4

Pythagorean Theorem does not work without more sides.

It is not a “special” triangle.

We must use trig !

feet?

50 feet

20o

Jared wants to know the height of the flagpole. He measures 50 feet away from the base of the pole and can see the top at a 20 degree angle. How tall is the pole?



Which of the 3 choices: sin, cos, tan uses the 50 and the x????

feetx

50 feet

20o

Tan 20 = x/50

Press tan 20 enter

So now we know

.364 = x/50

Multiply both sides by 50

X = 18.2 feet



Federal Laws specify that the ramp angle used for a wheelchair ramp must be less than or equal to 8.33 degrees.

feetx

3 feet

You want to build a ramp to go up 3 feet into a house.

What horizontal space will you need?

How long must the ramp be?



feetx

3 feet




8.33 o

feety

Sin 8.33 = 3/y

.145 = 3/y

.145y= 3

Y= 3/.145

Y=20.7 feet



feetx

3 feet




8.33 o

feety

tan 8.33 = 3/x

.146 = 3/x

.146x= 3

x= 3/.146

x=20.5 feet

using right triangle trigonometry (trig, for short!)

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