All categories

2 years ago

Find the number of distinct triangles with the measurements a = 8, b = 14, and A = 30°.

Mathematics

1 answer:

Maslowich2 years ago

5 0

Answer: 2

Step-by-step explanation:

By the law of sines,

$\frac{\sin B}{b}=\frac{\sin A}{a} \\ \\ \frac{\sin B}{14}=\frac{\sin 30^{\circ}}{8} \\ \\ \frac{\sin B}{14}=\frac{1}{16} \\ \\ \sin B=\frac{14}{16} \\ \\ B=\sin^{-1} \left(\frac{14}{16} \right), 180^{\circ}-\sin^{-1} \left(\frac{14}{16} \right) \\ \\ B \approx 61.04^{\circ}, 118.96^{\circ}$

Since either of these values for B will form a triangle (as A+B will be less than 180 degrees), 2 triangles can be formed with these measurements.

You might be interested in

Write the line (-5,-6) with slope 2/5 in point-slope form

stich3 [128]

Answer:

$y+6=\frac{2}{5} (x+5).$

Step-by-step explanation:

1) the common form of the point-slope form is y-y₁=s(x-x₁), where s - the slope, (x₁;y₁) - the point belongs to the required line;

2) if s=2.5; x₁= -5; y₁= -6, then the required equation is:

y+6=2/5(x+5).

5 0

3 years ago

The ratio of money in Terry's bank account to Faye's bank account was 3:7. Terry then put £220 in his account and Faye withdrew

Nadusha1986 [10]

Answer:

Terry initially had £390

Step-by-step explanation:

The ratio of the original amount is 3:7

Let the original amount Terry has be t and the original amount Faye has be f

3/7 = t/f

or simply 3f = 7t ••••••(i)

Terry putting 220 means he now has

t + 220

Faye withdrew 300

He now has f-300

These values are equal

t + 220 = f-300

f = t+220+300

f = t + 520 ••••••(ii)

Put ii into i

3(t + 520) = 7t

3t + 1560 = 7t

7t-3t = 1560

4t = 1560

t = 1560/4

t = 390

4 0

2 years ago

Which of the following equations uses the commutative property of addition to rewrite 1/3 + 2/5?

luda_lava [24]

The commutative property states that you can invert the order of the terms of a sum:

$a+b=b+a$

So, if you start with

$\dfrac{1}{3}+\dfrac{2}{5}$

Applying the commutative property you'll get

$\dfrac{2}{5}+\dfrac{1}{3}$

3 0

3 years ago

How do I solve this

Alina [70]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\displaystyle\sum \limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio} \end{cases} \\\\[-0.35em] ~\dotfill$

$\bf S_{20}=\displaystyle\sum \limits_{n=1}^{\stackrel{\stackrel{n}{\downarrow }}{20}}~\stackrel{\stackrel{a_1}{\downarrow }}{3}(\stackrel{\stackrel{r}{\downarrow }}{1.5})^{n-1}\implies S_{20}=3\left(\cfrac{1-1.5^{20}}{1-1.5} \right)\implies S_{20}=3\left(\cfrac{1-\stackrel{\approx}{3325.3}}{-0.5} \right) \\\\\\ S_{20}=3\left(\cfrac{-3324.3}{-0.5} \right)\implies S_{20}=3(6648.6)\implies S_{20}=19945.8$

8 0

3 years ago

Read 2 more answers

An investor bought an antique table for $6000. He paid 5% as a deposit and borrowed the remainder from a bank for two years at 1

Sloan [31]

First lets get rid of the deposit.
(0.95*6000)=5700

Formula is I=PRT
I= Interest earned
P=Principal amount (5700)
R=Rate (18% or 0.18 or 18/100)
T=Time period (2 years)
Equation:
I= 5700*2*0.18
I= 2052
But remember the question asks for monthly payments!
2052/24 (12 months in a year and T= 2 years)
Answer=$85.50

8 0

3 years ago

Find the number of distinct triangles with the measurements a = 8, b = 14, and A = 30°.​

Find the number of distinct triangles with the measurements a = 8, b = 14, and A = 30°.