1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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 :-).

You might be interested in
If x^2 = 49, then x^-2 =
Natalija [7]

Answer:

0.001665973

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Tom opens a bank account and makes an initial deposit of 500$. Then banker tells Tom that he is going to receive an annual rate
Arturiano [62]

~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases} \\\\\\ A=500\left(1+\frac{0.06}{1}\right)^{1\cdot 15}\implies A=500(1.06)^{15}\implies A\approx 1198.28

5 0
2 years ago
Two accounts earn simple interest. The balance y (in dollars) of Account A after x years can be modeled by y=10x 500. Account B
12345 [234]
In an installment loan, a lender loans a borrower a principal amount P, on which the borrower will pay a yearly interest rate of i (as a fraction, e.g. a rate of 6% would correspond to i=0.06) for n years. The borrower pays a fixed amount M to the lender q times per year. At the end of the n years, the last payment by the borrower pays off the loan.

After k payments, the amount A still owed is

<span>A = P(1+[i/q])k - Mq([1+(i/q)]k-1)/i, = (P-Mq/i)(1+[i/q])k + Mq/i. </span>The amount of the fixed payment is determined by<span>M = Pi/[q(1-[1+(i/q)]-nq)]. </span>The amount of principal that can be paid off in n years is<span>P = M(1-[1+(i/q)]-nq)q/i. </span>The number of years needed to pay off the loan isn = -log(1-[Pi/(Mq)])/(q log[1+(i/q)]). The total amount paid by the borrower is Mnq, and the total amount of interest paid is<span>I = Mnq - P.</span>
3 0
3 years ago
Determine a series of transformations that would map polygon ABCDE onto polygon A’B’C’D’E
zalisa [80]

Answer:

Reflected across x-axis followed by a dilation with a scale factor of 2 about the origin.

Step-by-step explanation:

It's clear from the graph,

Polygon ABCDE is reflected across x-axis then dilated so that it overlaps polygon A'B'C'D'E'

Let's choose a point A having coordinates (-2, -1)

By reflecting point A across x-axis,

Rule to be followed for the reflection,

(x, y) → (x, -y)

By this rule, coordinates of the image point A will be,

A(-2, -1) → A"(-2, 1)

Now point A"(-2, 1) has been dilated by a scale factor = k to form an image points A'(-4, 2).

Rule for the dilation of a point about the origin is,

A"(x, y) → A'(kx, ky)

A"(-2, 1) → A'(-2k, k)

Since, coordinates of point A' are (-4, -2),

Therefore, -2k = -4

k = 2

k = 2

Hence, polygon ABCDE was reflected across x-axis followed by a dilation with a scale factor of 2 about the origin to form polygon A'B'C'D'E'.

3 0
3 years ago
How do you solve 5 3/7 ÷ 5/11
Artyom0805 [142]

Answer:

11 33/35

Step-by-step explanation:

5 3/7 = 5 × 7/7 + 3/7 = 35 + 37 = 38/7

38/7 ÷ 5/11 = 38/7 × 11/5 = 38 × 11/7 × 5 = 418/35

418/35 = 11 33/35

Hope this helps!  

6 0
3 years ago
Other questions:
  • For each value of y, determine whether it is a solution to 18 &lt; or equal to 3y.
    10·1 answer
  • What is 246 divided by 3
    15·2 answers
  • A gumball machine contains 23 Green gumballs 52 red gum balls 34 blue gum balls 61 yellow gumballs and 30 pink gumballs what per
    12·1 answer
  • A physical education teacher plans to divide the seventh graders at Wilson Middle School into teams of equal size of year-ending
    9·1 answer
  • 6 1/3 - 5 4/9 what is this answer?​
    12·2 answers
  • Pls HELP I will give 20 points and brainliest
    11·2 answers
  • 15x^2+5x GCF help. out please
    10·1 answer
  • at 1 pm, you start out on your bike at 12 mph to meet a friend who lives 8 miles away. at the same time, the friend starts walki
    7·1 answer
  • Pls help I’m really confused on this last question
    12·2 answers
  • Determine the coordinates of Q(6, −4) after a reflection in the line x=2
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!