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evablogger [386]
3 years ago
14

In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC.

Mathematics
1 answer:
strojnjashka [21]3 years ago
6 0

Answer:

AB = 30 inch

BC = 14 inch or BC = 50 inch

Step-by-step explanation:

Make a drawing. Please see the attachment. All measurements are in inches.

Consider the two triangles:

∆ ABC and ∆ AB'C

1. Looking only at ∆ ABC. Since this is <em>not</em> a rectangular triangle, let's first consider ∆ ANC, so we can calculate NC.

AN is the height and there fore is perpendicular to NC and thus also to BC.

In ∆ ANC

AN² + NC² = AC²

We want to calculate NC, so:

NC² = AC² - AN²

Given: AC = 40 and AN = 24

NC² = 40² + 24²

NC² = 1600 + 576

NC² = 1024

NC = +-SQRT(1024)

NC = 32

NC = NB + BC

We want to know BC

BC = NC - NB

Given: NB = BN = 18 and we just calculated NC to be 32 so...

BC = 32 - 18

BC = 14

2. Looking only at ∆ AB'C

AN is the height and there fore is perpendicular to B'C. Let's consider ∆ AB'N, so we can calculate AB'.

AN is the height and there fore is perpendicular to B'N, which means it has an angle of 90° in ∆ AB'N.

In ∆ AB'N

c² = a² + b²

AB'² = AN² + B'N²

Given: AN = 24 and B'N = 18

AB'² = 24² + 18²

AB'² = 576 + 324

AB'² = 900

AB' = +-SQRT(900)

AB' = 30

In ∆ AB'C

with AB' = 30 and AC = 40

c² = a² + b²

B'C² = AB'² + AC²

B'C² = 30² + 40²

B'C² = 900 + 1600

B'C² = 2500

B'C = +-SQRT(2500)

B'C = 50

Now we have our answers.

Extra:

Please look at the picture again, but now concentrate on the indicated 50 and - 50...

I am trying to explain something about the meaning of the outcome of mathematical calculations like:

c² = 2500

c = +- SQRT(2500)

c = 50 or c = - 50

Depending on where you want to start from, you can "move" 50 inch in one direction or 50 inch in the opposite direction, hence the -50 inch. Please let me explain why I am making a fuss...

1). Let's consider ∆ AB'C. Going from B' to C, you "move" -50 inch form B' towards C. This 50 inch is what we calculated earlier, but the we neglected to explain why we discarded the minus value of the SQRT... We just stated it to be only the positive value! Normally we give no meaning to the negative variant of it... Well, is this true in this case?

2). Let's consider ∆ ABC'. Going from B to C', you "move" 50 inch form B towards C'. Please understand that the direction is opposite that of - 50 inch in 1).

It is important to understand that a negative sign means the 180° in the direction of the other way.

In general. When calculating a square side by using the SQRT, you carefully need to consider if you can discard the -

minus value of your calculated outcome.

Not always, but <em>usually</em> there is some sort of meaning to the negative part of the SQRT, you just need to be willing to understand what it possibly could mean.

I hope this has made some sense to you :-).

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How many times does 44 go into 6,668??? Plz
kherson [118]
151.54 is the answer
The 54 is underlined hence they repeat(use a calculator and you'll see).
3 0
3 years ago
A brand new video game system sells for $340. If the sales tax is 6.98%, how much will the new video game
tiny-mole [99]
$363.73
The sales tax is $23.73

Steps:
Sales tax is calculated by multiplying the purchase price by the sales tax rate to get the amount of sales tax due. The sales tax added to the original purchase price produces the total cost of the purchase.

So 340 • 6.89%
340• .0698= 23.732
If it’s a percentage you move the decimal two places to the left
340 + 23.73 = 363.73


Hope this helps
6 0
3 years ago
Error Analysis: Kayla said the remainder of x^3+ 2x^2 -4x + 6 divided by
andrezito [222]

9514 1404 393

Answer:

  C) No, Kayla is not correct, because the remainder is -49 not 149

Step-by-step explanation:

The remainder from division by x+5 can be found by evaluating the polynomial at x=-5, the value of x that makes the divisor zero.

Evaluation is often easier when the function is written in Horner form.

  ((x +2)x -4)x +6

For x=-5, this is ...

  ((-5 +2)(-5) -4)(-5) +6 = (-3(-5) -4)(-5) +6 = 11(-5) +6 = -49

Kayla is not correct; the remainder is -49.

5 0
2 years ago
You guysss pls help me
hichkok12 [17]

Answer:

option B)\frac{1}{12}

Step-by-step explanation:

According to the given conditions, the total number of outcomes are 24.

The probability that of drawing hearts card is

P=\frac{(total number of hearts cases)}{(total number of cases)}

total number of hearts cases= 6

thus P= \frac{6}{24} = \frac{1}{4}

now the probability of 4 or 6 is,

P=\frac{(total number of 4 or 6 cases)}{(total number of cases)}

thus P= \frac{8}{24} = \frac{1}{3}

thus, by multiplication law,

final probality is P= (\frac{1}{4})(\frac{1}{3})

P= \frac{1}{12}

5 0
3 years ago
16 is 10% of what number
marusya05 [52]

let's say is 16% of "x", meaning "x" is the 100%.

we know "x" is 100% and 16% of it is 10, so

\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 16&10 \end{array}\implies \cfrac{x}{16}=\cfrac{100}{10}\implies \cfrac{x}{16}=10\implies x = 160

6 0
3 years ago
Read 2 more answers
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