Mathematics

Question

Use the information to answer the questions.

In triangle ABC, a = 11 in., measure angle B=70 deg and

c = 9 in.

Which information about the triangle is given?
Use the information to answer the questions. In triangle ABC, a = 11 in., measure angle B=70 deg and c = 9 in. Which information about the triangle is given?

2 Answer

  • Answer:

    Part 1) The length of two sides and the measure of the included angle (Side-Angle-Side)

    Part 2) [tex]b^2=a^2+c^2-2(a)(c)cos(B)[/tex]  

    Part 3) [tex]b=11.6\ in[/tex]

    Step-by-step explanation:

    we have

    In the triangle ABC

    [tex]a=11\ in\\c=9\ in\\B=70^o[/tex]

    Part 1) Which information about the triangle is given?

    In this problem we have the length of two sides and the measure of the included angle (Side-Angle-Side)

    see the attached figure to better understand the problem

    Part 2) Which formula can you use ti find b?

    I can use the law of cosines

    [tex]b^2=a^2+c^2-2(a)(c)cos(B)[/tex]  

    we have

    [tex]a=11\ in\\c=9\ in\\B=70^o[/tex]

    substitute the given values

    [tex]b^2=11^2+9^2-2(11)(9)cos(70^o)[/tex]

    [tex]b^2=202-67.72[/tex]  

    [tex]b=11.59\ in[/tex]

    Part 3) What is b, rounded to the nearest tenth?

    Remember that

    To Round a number

    a) Decide which is the last digit to keep  

    b) Leave it the same if the next digit is less than [tex]5[/tex] (this is called rounding down)  

    c) But increase it by  [tex]1[/tex] if the next digit is  [tex]5[/tex] or more (this is called rounding up)

    In this problem we have

    [tex]11.59\ in[/tex]

    We want to keep the digit [tex]5[/tex]

    The next digit is [tex]9[/tex] which is 5 or more, so increase the "5" by 1 to "6"

    therefore

    [tex]b=11.6\ in[/tex]

  • Answer:

    Question 1:

    SAS

    Question 2:

    [tex]b^{2} =a^{2} +c^{2} -2ac * cos(B)[/tex]

    Question 3:

    11.6 in

    Step-by-step explanation:

    Edg2020

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