#1**+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°

CPhill
Aug 24, 2018

#2**+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

CPhill
Aug 24, 2018

#3**+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

CPhill
Aug 24, 2018

#4**+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

CPhill
Aug 24, 2018