+0

# Help!

0
200
4

Aug 24, 2018

#1
+107656
+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°

Aug 24, 2018
#2
+107656
+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

Aug 24, 2018
#3
+107656
+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

Aug 24, 2018
#4
+107656
+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

Aug 24, 2018