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Yuki888 [10]
3 years ago
10

1a) Use the pythagorean theorem tofind the missing side length.

Mathematics
2 answers:
victus00 [196]3 years ago
7 0

<u>Answer with step-by-step explanation:</u>

1a) We are given a right angles triangle and we are to find the missing side length using the Pythagoras Theorem.

x =\sqrt {(6)^2+(8)^2}

x=\sqrt {100}

x = 10

1b) Writing the sine, cosine and tangent for angles a and b:

sin a =\frac {8} {10}

cos a =\frac {6} {10}

tan a =\frac {8}{6}

sin b =\frac{6}{10}

cos b =\frac{8}{10}

tan b =\frac{6}{8}

Lana71 [14]3 years ago
5 0

Answer:

1)

a)

We are given one leg of triangle as 6 km and the other leg is of length of 8 km.

Hence, the hypotenuse is calculated using Pythagorean theorem as:

x^2=8^2+6^2\\\\\\x^2=64+36\\\\x^2=100\\\\x=10

Hence, the hypotenuse of the triangle or the missing side x=10 cm.

Now we calculate trignometric  ratio with respect to angle a and b as:

b)

We know that:

Sine of an angle is ratio of perpendicular to hypotenuse.

Cosine of an angle is ratio of base and hypotenuse.

And tangent of an angle is ratio of perpendicular and base.

<u>Angle a:</u>

We have perpendicular=8

Base=6

Hypotenuse=10

Hence,

sin a=8/10

cos a=6/10

tan a=8/6

<u>Angle b:</u>

Perpendicular =6

Base=8

Hypotenuse=10

Hence,

sin b=6/10

cos b=8/10

tan b=6/8

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sleet_krkn [62]

Answer:No

Step-by-step explanation:

Given system of equation is:

2x + 3 = y

2x + y = 15

To check whether (2,7) is solution to this system or not, we will put x=2 and y=7 in both equations.

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2(2) + 3 = 7

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Hence,

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2 years ago
A rectangular field on a farm is to be fenced in using the wall of the barn for one side and 200 meters of fencing for the other
vitfil [10]

Answer:

Rectangular area as a function of x :   A(x)  = 200*x  + 2*x²

A(max) = 5000 m²

Dimensions:

x = 50 m

l  = 100 m

Step-by-step explanation:

"x" is the length of the perpendicular side to the wall of the rectangular area to be fenced, and we call "l" the other side (parallel to the wall of the barn) then:

A(r) = x* l     and the perimeter of the rectangular shape is

P = 2*x + 2*l   but we won´t use any fencing material along the wll of the barn therefore

P  =  2*x + l       ⇒   200 = 2*x  + l      ⇒   l  = 200 - 2*x      (1)

And the rectangular area as a function of x is:

A(x)  = x * ( 200 - 2*x)  ⇒  A(x)  = 200*x  + 2*x²

Taking derivatives on both sides of the equation we get:

A´(x)  =  200 - 4*x     ⇒   A´= 0

Then    200 - 4*x  = 0     ⇒   4*x =  200   ⇒  x  = 50 m

We find the l value, plugging the value of x in equation (1)

l  = 200 - 2*x     ⇒ l = 200 - 2*50   ⇒  l = 100  m

A(max)  =  100*50

A(max)  = 5000 m²

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