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Please help! I am so confused. Sorry.

 Aug 24, 2018
 #1
avatar+98130 
+1

First one

We know the side opposite the missing angle and the hypotenuse....the trig function that relates these two is the sine

 

So  sine (?)  = 22 /41

 

And the sine inverse (arcsin) will give us the angle...so...

 

arcsin (22/41)  = ?  ≈ 32.45°

 

 

cool cool cool

 Aug 24, 2018
 #2
avatar+98130 
+1

Second one

We have an equilateral triangle  composed of three congruent triangles...

Each  has an included angle of 120°  between two sides of 28

 

The  area is  3*(1/2)(side)^2* sin (120°)  =

 

(3/2)(28)^2 * √3/2  =  

 

(3/4)(784)√3  =

 

588√3  units^2

 

 

cool cool cool

 Aug 24, 2018
 #3
avatar+98130 
+1

Third one

 

We have decagon  .... it is composed of 10 congruent triangles each with a base of 6yd

The height of each triangle is given by  3 / tan (18°)

 

So...the total area  is  10 (1/2)(base) (height)  =

 

10 (1/2) (6) (3/ tan (18°) =

 

90 / tan (18°)   ≈ 277 yd^2

 

 

cool cool cool

 Aug 24, 2018
 #4
avatar+98130 
+1

Last one

 

We have a hexagon with a perimeter of 30m....so.....each side  is  30 / 6  =  5m

 

And  we  have  6  congruent triangles  each with an included angle of 60° between two equal sides of 5m

 

So....the total area is

 

6(1/2) (5)^2 sin 60°  =

 

3 * 25 * √3/2  =

 

(3/2)*25√3 m^3  =

 

37.5√3 m^2 ≈  65 m^2

 

 

cool cool cool

 Aug 24, 2018

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