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KATRIN_1 [288]
3 years ago
9

Michelle’s house is 22 miles due north of Jan’s house and 30 degrees northeast of Richard’s house. Richard’s house is due east o

f Jan’s house. How far is it from Michelle’s house to Richard’s house?
Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
3 0

Answer:

Michelle’s house is 44 miles to Richard’s house.

Step-by-step explanation:

The distance can be found out by using the trigonometric ratio of sine theta

Sine theta= Perpendicular/ Hypotenuse

We know the values of hypotenuse and theta

Sine 30 = 22/ Hypotenuse

Hypotenuse= 22/ sine 30

Hypotenuse= 22/0.5

Hypotenuse = 44

The hypotenuse marks the distance between Michelle’s house to Richard’s house. Due east means counter clockwise rotation from east.

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Find the angle that the line through the given pair of points makes with the positive direction of the x-axis
Allisa [31]

Answer:

The answer to your question is Ф = 45°

Step-by-step explanation:

Data

A (1, 4)

B (-1, 2)

Process

1.- Find the slope of the line

formula

m = \frac{y2 - y1}{x2 - x1}

Substitution

m = \frac{2 - 4}{-1 - 1} = \frac{-2}{-2} = 1

Slope definition, is the steepness of a line and also is the tangent of the angle of the line.

                          tangent Ф  = slope

                          tangent Ф = 1

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4 0
3 years ago
Read 2 more answers
The vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). what is the perimeter and area in square units
ad-work [718]
Check the picture below.

the triangle has that base and that height, recall that A = 1/2 bh.

now as for the perimeter, you can pretty much count the units off the grid for the segment CB, so let's just find the lengths of AC and AB,

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&A&(~ 2 &,& 8~) 
%  (c,d)
&C&(~ 6 &,& 2~)
\end{array}~~~ 
%  distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AC=\sqrt{(6-2)^2+(2-8)^2}\implies AC=\sqrt{4^2+(-6)^2}
\\\\\\
AC=\sqrt{16+36}\implies AC=\sqrt{52}\implies AC=\sqrt{4\cdot 13}
\\\\\\
AC=\sqrt{2^2\cdot 13}\implies AC=2\sqrt{13}

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&A&(~ 2 &,& 8~) 
%  (c,d)
&B&(~ 16 &,& 2~)
\end{array}\\\\\\
AB=\sqrt{(16-2)^2+(2-8)^2}\implies AB=\sqrt{14^2+(-6)^2}
\\\\\\
AB=\sqrt{196+36}\implies AB=\sqrt{232}\implies AB=\sqrt{4\cdot 58}
\\\\\\
AB=\sqrt{2^2\cdot 58}\implies AB=2\sqrt{58}

so, add AC + AB + CB, and that's the perimeter of the triangle.

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Answer:

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Step-by-step explanation:

mafioaso.

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Step-by-step explanation:

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And if both together then

Probability = 2/6 = 1/3

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