Cholkar     MCHS   MATH II       ___/___/___         Name____________________________
U7L1INV2	How can trigonometric functions be used to calculate heights?	
HW # 
	Complete Handout & CYU pg. 471; pg. 485 # 32, 34, 35 [3, 6, 7, CYU, 32] 
                      	
Do Now

	Consider the line that contains the origin and the point with coordinates (3, 4).
a.  Sketch the line.

b.  Label the angle formed by the line and the positive x-axis θ. Without using your calculator, express the following in ratio form.

          tan θ =                          cos θ =                               sin θ =

http://www.youtube.com/watch?v=Zs_R7zYuaOk (clinometers)	
  INVESTIGATION:  MEASURING WITHOUT MEASURING  (pg. 467)
My role for this investigation _________________________

1.  a.  Use the given information to calculate the lengths of 

b.  

_________________________________________________________________________________________

2.  a.  Explain why the following right triangle definitions of sine, cosine, and tangent make sense.

__________________________________________________________________________________________

__________________________________________________________________________________________

b.  Write expressions for tan B, sin B, and cos B.

3.  Chicago’s Bat Column, a sculpture by Claes Oldenburg, is shown 
to the right.  

a.  About how tall do you think the column is?  What visual clues in the 
photo did you use to make your estimate?

____________________________________________________________

b.  In the diagram to the right, what lengths and angles could you determine easily by direct measurement?

_________________________________________________________________________________

c.  Which trigonometric functions of  involve side ?  Of these, which also involve a measurable length?

__________________________________________________________________________________

d.  Which of the trigonometric functions of  involve side  and a measurable length?  If you know the measure of angle of elevation , how can you find the measure of ?

_________________________________________________________________________________________

e.  To find the height of Bat Column, Krista and D’wan proceeded as follows.  First, Krista chose a spot (point A) 20 meters from the sculpture (point C).  D’wan estimated the angle of elevation at A by sighting the top of the sculpture along a protractor and using a weight as shown.  He measured to be 55 .  What is the measure of  ?

_________________________________________________________________________________________

f.  They next used the following reasoning to find the height BC.

i.  Why did they decide to use the tangent function rather 
than the sine function?
_________________________________________________

ii.  How did the know that tan 55=1.4281?  __________________________________

iii.  Check that each step is correct in their reasoning.

iv.  How do you think Krista and D’wan used this information to calculate the height of Bat Column?

_________________________________________________________________________________________

g.  Ken said he could find the length AB (the line of sight distance) by solving 

i.  Use Ken’s idea to find the length AB.  ________________________________

ii.  What is another way you could find AB by using a different trigonometric function?  __________________

iii.  Could you find AB without using a trigonometric function?  Explain.  

__________________________________________________________________________________________
4.  Write two equations involving trigonometric functions of acute angles that include s and the indicated length.  Then rewrite each equation in an equivalent form “s =….”

			_______________________		__________________________

			_______________________		__________________________

			_______________________		__________________________

5. a.  

b.  Use your calculator to find the sine, cosine, and tangent of 66.  Of  54.  Compare these results with those in the table on page 465.

_____________________________________________________________

6.  

Lesson Summary	

The trigonometric ratios sine, cosine, and tangent are useful in calculating lengths in situations modeled with right triangles.  Refer to the right triangle below in summarizing your thinking about how to use trigonometric functions in the situations described.

	

Math Toolkit Vocabulary:  angle of elevation, SOHCAHTOA

Cholkar     MCHS   MATH II       ___/___/___         Name____________________________

HW # 

1.  Using the following pictures, write the trigonometric equation that includes the indicated angle and sides:	
a.	

	b.	
	c.	
	
2.	Manipulate the following equations so that x is all by itself.  DO NOT use a calculator to find a value for x.	
	a.	

	b.		
	c.	

	d.		

CYU pg. 471  

REVIEW:   pg. 485 # 32, 34, 35