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3 years ago

A parallelogram has sides of 18 and 26 ft, and an angle of 39° . Find the shorter diagonal

Mathematics

1 answer:

Fed [463]3 years ago

3 0

Answer:

16.51

Step-by-step explanation:

In a parallelogram, the opposite angles are always equal in measure. So two of the angles in the parallelogram measure 39 degrees each.

The sum of angles of the parallelogram must be 360 degrees. Let the other two angles be x degree each. We can set up the following equation for the angles:

39 + 39 + x + x = 360

78 + 2x = 360

2x = 282

x = 141

This means, the other two angles measure 141 degree each. The shorter diagonal will be opposite to the shorter angle.

Hence, the diagonal opposite to the angle 39 degree will be the shorter one. A diagonal divides the parallelogram in two triangles. So we will have two sides and an included angle and we have to find the third side of the triangle which can be found using the law of cosines. Let the third side be c as shown in image below, using the law of cosines, we can write:

$c^{2} = a^{2}+ b^{2} -2ab cos(\gamma)\\\\c^{2}=18^{2}+26^{2}-2(18)(26)cos(39)\\\\ c^{2}=272.59\\\\ c=16.51$

Thus the shorter diagonal will be 16.51 feet in measure.

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Answer:

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Step-by-step explanation:

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3 years ago

If the null hypothesis is true in a chi-square test, discrepancies between observed and expected frequencies will tend to be

babymother [125]

Answer:

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Here in this question, we want to state what will happen if the null hypothesis is true in a chi-square test.

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3 years ago

Answers fast please. 1.) y=x−63x+2y=8 Use the substitution method. A.) (4, −2) B.) (14, 8) C.) (0, −6) D.) (3, −3) 2.) What is t

GrogVix [38]

QUESTION 1

The given system of equation is

$y=x-6...eqn1$

and

$3x+2y=8...eqn2$

Let us substitute equation (1) into equation (2) to get,

$3x+2(x-6)=8$

We expand the bracket to get,

$3x+2x-12=8$

We simplify to get.

$5x-12=8$

We group like terms to get

$5x=8+12$

$\Rightarrow 5x=20$

$\Rightarrow x=4$

We now substitute $x=4$ in to equation (1) to obtain,

$y=4-6=-2$

The correct answer is option A.

QUESTION 2

The given system of equations is

$y-x=9...eqn1$

and

$10+2x=-2y...eqn2$

We make y the subject in equation (2) to get,

$y=-x-5..eqn3$

We put equation (3) into equation (1) to obtain,

$-x-5-x=9$

We group like terms to get,

$-x-x=9+5$

This implies that,

$-2x=14$

We divide through by $-2$ to get,

$x=-7$

Hence the x-coordinate is $-7$

QUESTION 3

The given system is

$y=3x-1..eqn1$

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$x-y=-9...eqn2$

We make $x$ the subject in equation (2) to get,

$x=y-9...eqn3$

We put equation (3) into equation (1) to obtain,

$y=3(y-9)-1$

We expand the bracket to get,

$y=3y-27-1$

Group like terms to get,

$y-3y=-27-1$

We simplify to get;

$-2y=-28$

This implies that,

$y=14$

Therefore the y-coordinate is 14.

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