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°
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
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
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