Dragan

Let rhombus side be       c = 4

1/2 of short diagonal       a = 1.45

1/2 of long  diagonal        b = ?

We have the right triangle  

Larger angle  β = ?                    cos(β/2) = a / c =68.74619°

                                                              β = 137.4923816°     

IT IS TOTALLY______

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In △ABC, D lies on BC⎯⎯⎯⎯⎯⎯⎯⎯ such that BD=32CD. If AB=2AC and AD=32CD, what is the value of cos∠ADC (enter answer in fraction form)?

AB = 62.225

AD = BD = 32

CD = 1

AC = 31.1125

∠DAB = ∠DBA = 13.523277°

∠ADC = 27.046554°

cos∠ADC = 0.89063735   ≈  89 / 100   

https://web2.0calc.com/questions/help-please-thx_4#r4

YZ ≈ 9.428  

A circle with radius 6 has a sector with a central angle of 48º.  What is the area of the sector?

Area of the sector:   A = [ (r² * pi) / 360 ] * 48  

2)    Angle  EDC = 15º  

Working alone and at a constant rate, Machine A takes 3 hours to create a widget. Machine B, working alone and at a constant rate, takes x hours to create a widget. Working together, Machine A and B take 12 hours to build two widgets. What is the value of x?

Machine B is 3X slower than machine A

3 + x = 12        x = 9  

Let be P the centroid of triangle ABC. If triangle ABP is an equilateral triangle with a side length of 2, then find the perimeter of triangle ABC.

AB = 2

PF = sqrt(3)

CF = PF * 3

AC = BC = sqrt[(AF)² + (CF)²]

Perimeter of triangle ABC = AB + AC + BC    

1)  A circle centered at A with radius 10 is externally tangent to a circle centered at B with radius 7. A line that is externally tangent to both circles intersects line AB at C. Find the length BC.

BC = 39.66666672   

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2)           AB = 2        x = 1       CD = 4.5     y = 2.25    

             r = sqrt ( xy ) = sqrt ( 1 * 2.25 ) = 1.5   

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3)           XY = 14            WX = 8

tan(Y) = 8 / 14        ∠Y = 29.7448813°

XZ = tan(Y) * WX = 4.571428571

YZ = XY - XZ = 9.428571429

YZ ≈ 9.428      

At Glenridge High School, 20 percent of the students are seniors. If all of the seniors attended the school play, and 60 percent of all the students attended the play, what percent of the non-seniors attended the play?

This question is very  t r i c k y

100%   -   all students at Glenridge High School

20%    -    seniors, and all of them attended the play

Out  of  80% of non-seniors, only one half of them  attended the play.

Answer:    50% of non-seniors attended the play.    

In triangle ABC, AB=13, AC=14 and  BC=15. Let I be the incenter. The incircle of triangle ABC  touches sides BC, AB, and AC at D, E, and F, respectively. Find the area of quadrilateral AEIF.

AB = 13        AC = 14       BC = 15

I     c     I       I      b     I      I     a     I

Semiperimeter    s = ( a + b + c )/2 = 21

Triangle (ABC) area is:    A = sqrt [ s (s-a)(s-b)(s-c)]  = 84 u²

Radius   r = A / s   = 4

Angle   BAC =>           cos(∠A) = ( b² + c² - a² ) / 2bc   = 67.38°

AE = AF  = r / tan (∠A/2)  = 6

Area of quadrilateral  AEIF  = AF * r  = 24 u²