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Mathematics

1 answer:

Irina-Kira [14]3 years ago

6 0

Search the question on the internet and ask if which it is out of them both answers and there you go

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Leto [7]

Answer:

DA = 285.7 m

Step-by-step explanation:

First we need to find the side AB in the triangle ABC, and we can do this using Pythagoras' theorem:

AB^2 = BC^2 + AC^2

AB^2 = 300^2 + 400^2

AB^2 = 25000

AB = 500 m

We can find the angle ABC with the tangent relation:

tangent(ABC) = 400/300 = 4/3

ABC = 53.13°

From triangle ABC, we have:

ABC + BCA + CAB = 180°

53.13 + 90 + CAB = 180

CAB = 36.87°

From triangle DAC, we have:

DAC + ACD + CDA = 180

36.87 + 45 + CDA = 180

CDA = 98.13°

Now to find the side of DA, we can use law of sines in triangle DAC:

DA/sin(DCA) = AC/sin(CDA)

DA/sin(45) = 400/sin(98.13)

DA = 400 * 0.7071 / 0.9899 = 285.7258 m

Rounding to nearest tenth, we have DA = 285.7 m

3 0

3 years ago

Quadrilateral ABCD is inscribed in this circle.

Alecsey [184]

The sum of all interior angles in a polygon is

180(n-2), where n = sides, well, this is a QUADrilateral, so it has 4 sides, so the total is 360°.

now, let's find what angle C is first,

$\bf \stackrel{A}{(2x-40)}+\stackrel{B}{(116)}+C+\stackrel{D}{(x)}=360\implies C+3x+76=360
\\\\\\
C+3x=284\implies C=284-3x$

now, recall the "inscribed quadrilateral conjecture", where opposite angles are "supplementary angles", thus

$\bf \stackrel{\measuredangle A}{(2x-40)}+\stackrel{\measuredangle C}{(284-3x)}=180\implies -x+244=180
\\\\\\
64=x\\\\
-------------------------------\\\\
\measuredangle A=2(64)-40$

8 0

3 years ago

Read 2 more answers

The area of a square garden is 1/81 km2. How long is each side

Alex_Xolod [135]

I hope this helps you