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

### 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

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 = 6 + 12

→ CA = 18

• 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

DC = 12

solving for DE

CD/DE = AC/AB

12/DE = 18/17

204 = 18DE

• 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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