casey preguntado en Science & MathematicsMathematics · hace 1 mes

THICC BRAINS NEEDED?

this is the math problem, and i need help solving it step by step please i’m gonna cry

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9 respuestas

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  • hace 1 mes
    Respuesta preferida

    The triangles (ABC and DEC) are similar, so all measurements will be in the same proportion.

    In the small triangle (DEC), the longest side is 20 units.

    In the big triangle (ABC), the longest side is 30 units (10+20 = 30)

    So the proportion of the small triangle compared to the big triangle is 20/30 = 2/3.

    To find DE, take 2/3 of AB

    2/3 * 17 = 34/3 = 11 1/3

    For DC, the proportion of x to x+6 is also 2/3:

    x / (x+6) = 2/3

    Cross multiply:

    3x = 2(x + 6)

    3x = 2x + 12

    3x - 2x = 12

    x = 12

    Another way to see that is to notice that CE (20) is twice the length of EB (10). So it makes sense that DC will be double DA (6).

    2 * 6 = 12

    Answer:

    DC = 12

    DE = 11 1/3

    P.S. Don't assume this is a right triangle, by the way. It may look like that in the diagram but it is clearly not a right triangle if you check.

  • hace 1 mes

    The little triangle (CDE)

    CD ?

    DE ?

    CE = 20

    The big triangle (ABC)

    CD becomes CA

    DE becomes AB

    CE becomes CB

    Given that the angle_1 and the angle_2 are similar, you can deduce that:

    CD * ratio = CA ← equation (1)

    DE * ratio = AB ← equation (2)

    CE * ratio = CB ← equation (3)

    The equation (3) gives us:

    CE * ratio = CB

    20 * ratio = 20 + 10

    ratio = 30/20

    ratio = 3/2

    The equation (1) gives us:

    CD * ratio = CA

    CD = CA/ratio → where: CA = CD + DA = CD + 6

    CD = (CD + 6)/ratio → recall: ratio = 3/2

    CD = (CD + 6)/(3/2)

    CD = (CD + 6) * (2/3)

    3.CD = 2.(CD + 6)

    3.CD = 2.CD + 12

    → CD = 12

    AC = AD + DC

    AC = 6 + 12

    → CA = 18

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  • hace 1 mes

    solve for DC

    DC/CE = AC/BC

    x/20 = (x + 6)/30

    30x = 20(x + 6)

    30x = 20x + 120

    30x - 20x = 120

    10x = 120

     x = 12  Answer//

    DC = 12

    solving for DE

    CD/DE = AC/AB

    12/DE = 18/17

    204 = 18DE

    DE = 11 1/3 Answer//

  • hace 1 mes

    As the triangles are in proportion and similar, we know interior angles are identical and the side lengths are in proportion.

    So, no trigonometry is required.

    Now, as the lengths are in propotion we have:

    CD/CA = CE/CBso, x/(x + 6) = 20/(20 + 10)i.e. x/(x + 6) = 2/3so, 3x = 2(x + 6)=> 3x = 2x + 12Hence, x = CD = 12Then, DE/AB = 2/3so, DE/17 = 2/3=> DE = 34/3Hence, DE = 11 1/3:)>

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  • hace 1 mes

    By Pythagorean Theorem

    AC  =  sqr( 30 ² - 17 ² )

    AC = 24.7184

    X =  24.7184 - 6

    X =  18.7184

  • hace 1 mes

    ΔABC ~ ΔDEC

    θ1 (angle 1) = θ2 (angle 2)

    DC = x

    AC = x + 6

    cos θ1 = 17 / (10 + 20)

    cos θ1 = 17 / 30

    cos θ1 = 0.566666667

    arccos (0.566667) = 55.48189216 ° ≈ 55.5 °

    θ1 = 55.5 °

    θ2 = 55.5 °

    sin θ2 = x / 20

    sin 55.5° = x / 20

    20(sin 55.5°) = x

    x = 20(sin 55.5°)

    x = 20(0.823947)

    x = 16.47894 ≈ 16.5

    x = DC = 16.5 ANSWER

    cos θ2 = DE / 20

    20(cos θ2) = DE

    DE = 20(cos θ2)

    DE = 20(0.56667)

    DE = 11.33334 ≈ 11.3 ANSWER

  • hace 1 mes

     △ ABC ~ △DEC 

     ∠1 and ∠2 have the same measure 

     Find DC and DE 

     AB = 17

     Let DC = x and AC = x + 6

     CD/CA = DE/AB = 20/30

     30x = 20(x + 6)

      x = 12

     DC = 12

     DE = 11 1/3

     

  • hace 1 mes

    CB=30 and CE=20 and EB=10

    so

    (EB/CB)=(1/3) and (CE/CB)=(2/3)

    x=(2/3)6=4

  • Anónimo
    hace 1 mes

    When God was handin' out thicc brains, I musta been standin' in the wrong line, 'cause what I got was a dicc brain.

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