Find the height of an equilateral triangle with sides of length 12

Mathematics

2 answers:

Licemer1 [7]2 years ago

8 0

10.4 centimeters I did the problem my self

MAVERICK [17]2 years ago

4 0

Answer:

Answer

sqrt(108)

6 sqrt(3)

10.3923

I don't know which answer you want.

Step-by-step explanation:

Drop a perpendicular from the top angle to the base.
The base is cut into 2 equal parts.
Each part is 12/2 = 6
The perpendicular, as its name implies, meets the base at 90o.
You can use the Pythagorean Theorem to find the height.

h^2 = side^2 - (1/2 b)^2

h^2 = 12^2 - 6^2

h^2 = 144 - 36

h^2 = 108

Take the square root of both sides

h = sqrt(108)

h = sqrt(2*2 * 3 * 3 * 3)

h = 2 * 3 sqrt(3)

h = 6sqrt(3)

h = 6 * 1.7321

h = 10.3923

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Please show me how to solve the initial value problem <br> y'=tanx y(pi/4)=3

AlexFokin [52]

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$\dfrac{\mathrm dy}{\mathrm dx}=\tan x\iff\mathrm dy=\tan x\,\mathrm dx$

Integrating both sides gives the general solution.

$\displaystyle\int\mathrm dy=\int\tan x\,\mathrm dx$
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Given that $y\left(\dfrac\pi4\right)=3$ , we have

$3=-\ln\left|\cos\dfrac\pi4\right|+C$
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and so the particular solution to the IVP is

$y=-\ln|\cos x|+3-\ln\sqrt2$
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