M2 PS 32 Solutions

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NYS COMMON CORE MATHEMATICS CURRICULUM
M2
Lesson 32
GEOMETRY
Lesson 32: Using Trigonometry to Find Side Lengths of an Acute Triangle
Date: 10/28/14
482
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Exit Ticket Sample Solutions
Use the law of sines to find lengths and in the triangle below. Round answers to the nearest tenth as necessary. 1.
  
 
 
 
 
  
 
   
   
   
   
Given  , use the law of cosines to find the length of the side marked to the nearest tenth. 2.
    
  
   
    
 
Problem Set Sample Solutions
1. Given  ,  ,    , and    , calculate the measure of angle to the nearest tenth of a
degree, and use the law of sines to find the lengths of  and  to the nearest tenth.
By the angle sum of a triangle,    .
 


 
 
 

    
   
     
  
NYS COMMON CORE MATHEMATICS CURRICULUM
M2
Lesson 32
GEOMETRY
Lesson 32: Using Trigonometry to Find Side Lengths of an Acute Triangle
Date: 10/28/14
483
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Calculate the area of   to the nearest square unit.
 
 
 
   
       
2. Given  ,   , and  , calculate the measure of , and use the Law of Sines to find the lengths of

and 
to the nearest hundredth.
By the angle sum of a triangle,   .
 
 
 
 
  
    
  
 
  
    
   
3. Does the law of sines apply to a right triangle? Based on  , the following ratios were set up according to the
law of sines.
 
 
 
Fill in the partially completed work below:
 

 

  
 

 

  
What conclusions can we draw?
The law of sines does apply to a right triangle. We get the formulas that are equivalent to   
 and
  
, where and are the measures of the acute angles of the right triangle.
NYS COMMON CORE MATHEMATICS CURRICULUM
M2
Lesson 32
GEOMETRY
Lesson 32: Using Trigonometry to Find Side Lengths of an Acute Triangle
Date: 10/28/14
484
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
4. Given quadrilateral ,   ,   ,   ,  is a right angle and   , use the Law
of Sines to find the length of , and then find the lengths of 
and 
to the nearest tenth of an inch.
By the angle sum of a triangle,   ; therefore,
  is an isosceles triangle since its base 's have equal
measure.
 
 
    
   
    
   
5. Given triangle ,  ,  , and   , use the Law of Cosines to find the length of 
to the
nearest tenth.
     
   
  
     
  
  
6. Given triangle ,   ,   , and   . Draw a diagram of triangle , and use the law of cosines
to find the length of 
.
   
  
   
     
 
The length of 
is approximately  .
Calculate the area of triangle .
 

 
 
    
   
The area of triangle  is approximately   square units.

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