Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

The length of the sides of a triangle are 8, 8, and 3. What is the measure of the smallest angle in the triangle?

A)20.6

B)21.6

C)22.0

D)28.4

E)33.8

* There is clearly something wrong with the way i solved this, i used the Law of Cosines, the answer i got os none of these five. It would be great if someone explained. Thanks:)

9 Answers

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  • 2 months ago
    Favorite Answer

    Simple mistakes are made by many when using the cosine rule. However, you need to show your workings so we can identify where your mistakes are being made.

    Anyway, the smallest angle is opposite the shortest side so,

    3² = 8² + 8² - 2(8)(8)cosθ

    so,  128cosθ = 8² + 8² - 3²

    i.e.  128cosθ = 119

    Hence, cosθ = 119/128

    so, θ = cos⁻¹(119/128) => 21.6°

    :)>

  • 2 months ago

    Use the Cosine Rule

    3^2 = 8^2 + 8^2 - 2(8)(8)CosA 

    9 = 64 + 64 - 128CosA 

    CosA = (9 - 64 - 64 ) / -128 

    CosA = -119/-128 

    CosA = 119/128 

    CosA = 0.92968...

    A = Cos^-1( 0.92968...) 

    A = 21.613845... degrees.  

  • 2 months ago

    8x8x3 , none its cant be that size .

  • 2 months ago

    Since the triangle is isosceles, A/2 = sin⁻¹(1.5/8) = 10.8º. The smallest angle A = 2*10.8º = 21.6º

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  • Bill-M
    Lv 7
    2 months ago

    Triangle with Three sides Known (SSS) -

    The Angles are:  79.19 /  79.19 and 21.6

    Use the Law of Cosines First to find one of the Angles. Then use the Law of Cosines again to find another Angle.  The last angle is found by 180 - A - B.

    COS A = (8^2 + 8^2 - 3^2) / 2*8*8

    COS A = (64 + 64 - 9) / 128

    COS A = 0.9297

    A = COS^-1 (0.9297)

    A = 21.6138

  • 2 months ago

    Let the small angle be A, then

    cosA=(8^2+8^2-3^2)/(2*8^2)

    =>

    cosA=1-9/(2*64)=0.9296875

    =>

    A=cos^-1(0.9296875)=21.6 (B)

  • 2 months ago

     The length of the sides of a triangle are 8, 8, and 3.   

     c^2 = a^2 + b^2 − 2ab cos (C)

     9 = 64 + 64 − 2(64) cos (C)

     cos (C) = 119/128

     C = 34.2675° (degrees)

     B or C = 21.465° (degrees)

     The measure of the smallest angle in the triangle:

     21.465° (degrees)

  • Philip
    Lv 6
    2 months ago

    Visualize 2 8'' arms of an isosceles triangle descending from the apex to opposite ends of a 3'' base. Label the apex A and base BC. Sides are labeled as a,b and c where a = BC, b = AC and c = AB. By law of cosines we have 

    a^2 = b^2+c^2-2bc*cosA. Then cosA = (b^2+c^2-a^2)/2bc. Here a = 3, b=c=8.

    cosA=(8^2+8^2-3^2)/128=119/128 so A = arccos(119/128) = 21.61384575 deg

    The smallest side is opposite the smallest angle and visa-versa. That's why I

    chose the apex angle as the smallest angle in the triangle. Correct answer is B).

  • Anonymous
    2 months ago

    Shortest edge has smallest angle.

    angle A = acos((b.b+c.c-a.a)/(2bc)), Law of Cosines

    = acos((8.8.2-3.3)/(2.8.8) 

    = 21.6 degrees answer B.

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