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inna [77]
4 years ago
6

Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the value of n to the nearest whole number? 18 22 29 41

Mathematics
2 answers:
nalin [4]4 years ago
4 0
We know that
applying the law of cosines
a² = b²+ c²<span> – 2*b*c*cos(A)
</span>
in this problem
a=?
b=20
c=9
A=90°
so
a² = b²+ c² – 2*b*c*cos(A)
but
cos (A)=0
a² = b²+ c²-----> 20²+9²----> a²=400+81----> a²=481-----> a=√481
a=21.93-----> a=22

the answer is
22

vampirchik [111]4 years ago
3 0

B. 22

Law of cosines: a2 = b2 + c2 – 2bccos(A)

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will show you two (2) ways to solve this problem.

A diagram is needed to see what is going on....

 

Without loss of generality (WLOG)

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The measure from the bottom of the ladder to the wall is 6.

 

 

Option 1:

 

The ladder, ground and wall form a right triangle.

 

The hypotenuse (ladder) is 14 feet.

 

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  so the base of this right triangle is 6 feet.

 

The top of the ladder to the ground represents

the missing leg of the right triangle.

 

The pythagorean theorem applies, which says

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36 + h^2 = 196

 

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   = sqrt(16 * 10)

 

    = sqrt(16)* sqrt(10)

 

    = 4*sqrt(10) <--- exact answer

 

    = 4 * 3.16227766016838....

 

     = 12.64911....

 

    12.65 <--- rounded to 2 digits as directed

 

----------------------------------------------

Option #2: using trig

 

With respect to the angle formed by the bottom of the

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  cos T = 6/14 = 3/7  

 T = inverse-cosine(3/7) = 64.623006647 degrees

 

 sin(64.623006647) = h/14

 

 h = 14*sin(64.62300647) = 12.6491106 <--- same answer                        

hope this helps

Step-by-step explanation:

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