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lina2011 [118]
3 years ago
14

Consider the right triangle ABC given below: The altitude divides triangle ABC into two smaller right triangles, and all three t

riangles are 45-45-90 triangles
i. What is the length of the BC (x in the picture)?

ii. What is the length of CD (y in the picture)?

iii. What is the length of BD (z in the picture)?

Please Show Your Work

Mathematics
1 answer:
yKpoI14uk [10]3 years ago
4 0

Answer:

x =8

y = 4sqrt(2)

z = 4sqrt(2)

Step-by-step explanation:

The easiest one to calculate is x

If it is a 45 -45-90 degree triangle then AB = BC=x

Since AB =8  then BC =8  and x=8

The next easiest to calculate is z

If it is a 45 -45-90 degree triangle then AD = BD=z

Using the Pythagorean theorem

z^2 +z^2 = 8^2

2z^2 =64

Divide by 2

x^2 = 32

Taking the square root of each side

z = sqrt(16)sqrt(2)

z=4sqrt(2)

Finally, we can find y

If it is a 45 -45-90 degree triangle then BD = DC

BD =z =4 sqrt(2) = DC = y

Therefore y =4 sqrt(2)

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Which point is collinear with points a and d
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B. (6, -8)

First, you need to figure out the slope of the line

(y1 - y2) / (x1 - x2)

After substituting points D(-3, 4) A(3, -4)

[4 - (-4)] / (-3 - 3)
(8) / (-6)

The slope of the line is -8/6 or -4/3 simplified

Then you can put it in point slope form:

(y - y1) = m(x - x1)

(y - y1) = -4/3(x - x1)

The point that I am using for point slope form is A(3, -4)

[y - (-4)] = -4/3(x - 3)
y + 4 = -4/3(x - 3)

Next you have to simplify the equation so that y is isolated

y + 4 = -4/3(x - 3)

First distribute the -4/3

y + 4 = -4/3(x) + (-4/3)(-3)
y + 4 = -4/3x + 4

Subtract 4 on both sides
y + 4 - 4 = -4/3x + 4 - 4
y = -4/3x

Now that you have y = -4/3x, you can substitute the values until one of them makes the equation equal

For example) (6, -8)
-8 = -4/3(6)
-8 = -8

So since (6, -8) fits in the slope intercept equation, it must me collinear with points A and D

~~hope this helps~~

6 0
3 years ago
I need help with this plz.
valina [46]

Answer:

what do u need help with?

Step-by-step explanation:

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Rewrite the equation in Ax+By=c <br> y-4=5(x-6)
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Help me please i’ll rate brainliest
Cloud [144]

Answer:

<em>- 1.568</em>  

Step-by-step explanation:

Let's assume that the base of the given logarithm is 10.

log m = 0.345 ⇒ 10^{0.345} = m

log n = 1.223 ⇒ 10^{1.223} = n

mn = 10^{0.345} × 10^{1.223} = 10^{1.568}

\frac{1}{mn} = 10^{-1.568}

log 10^{-1.568} = - 1.568 × log 10 = <em>- 1.568</em>

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3 years ago
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