Dragan

https://web2.0calc.com/questions/please-help_50731#r2

four ways to get to 8 in just using the number 2,3 and 4

1)     2⁰ + 3 + 4 = 8

2)     2 * 3 + √4 = 8

3)     ( 2 * 3 * 4 ) / 3 = 8

4)      3² -  (√4) / 2  = 8    

1)    The angle bisector theorem:    CY / AY = BC / AB

                                                    4 / 6 = BC / 8

                                                     BC = 5.333333

2)    Using a Law of cosines calculate angles C  and  B

3)    Use the Law of sines to calculate BZ

Geometry is fun.

You don't need the law of sines, you need this:

15m / tan(55º) ≈ 10.5 m  

To prove that the shaded area is equal to the area of a triangle (ABC), we have to find the area of the entire figure, and then subtract the area of the largest semicircle.

Let the sides of a triangle ABC be 3-4-5

Let denote the areas of 3 semicircles, starting with the smallest one:    A₁, A₂, and  A₃

A₁ = (1.5²*pi) /2 = 3.534291735 u²

A₂ = 2pi = 6.283185307 u² 

A₃ = (2.5²*pi) /2 = 9.817477043 u²

ΔA = (3*4) /2 = 6 u²

ΔA = ( A₁ + A₂ + ΔA ) - A₃

6 = 6  

I'll give you a few hints:

1)    Draw an altitude h from D to a point F on line segment  AM.      h = 2r

2)   Find the lengths of  lines AF and FM

3)   Use the Pythagorean theorem to find the length of DM.  

(btw., ignore those suggested answers; the length of DM is totally different from those numbers.)

V = [(3+8)/2] * 4 * 4.3  

2)              first triangle              17--30--17

                 second triangle         17--16--17     

" slightly"?!    area of a circle is exactly  10pi

r = sqrt( 10 ) = 3.16227766            angle (AOB) = 360º - 215º = 145º

A = 145º/360º * pi * r² = 12.65363708

A ≈ 12.654 

Excellent work!!!