Plz help with math thank you

Step-by-step explanation:

Law of Sines  recall   Sin(A) /a  = Sin(B) /b  

does the above make sense?

Next we need to find  the angle of A

notice that 16+75=91  :o

so angle A is only 89° ..(b/c all the way around then inside of a triangle is 180)  so this is NOT a right triangle but that's okay, b/c law of sines still works fine.

then we want to find length of line AB

and if 89 = A  then a = BC

and if  75 = B the  b = AB (note that in the given triangle this is angle C, i'm using B , b/c you can see the difference between capital B and  lower case b much easier than you can with C, & c  :/   )

capitals are the angles while lower case are the length of the sides

then

Sin(89) / 29 = Sin(75) / b

solve the parts that can be put into numbers or solve for 'b' first, that means isolate 'b' all by itself on one side of the equal sign .

0.034477 = 0.965925/ b

b = 0.965925 / 0.034477

b = 28.0165

b = 28.0 ( to the nearest 10th)

we have the parts to plug in now

Sin(75) /

The lateral Surface area of the cylinder is 162.2 cm².

The lateral Surface area of the triangular prism is 226.6 cm².

Step-by-step explanation:

To find the lateral Surface area of the cylinder :

The given information are,

The height of the cylinder, h = 12.3 cm.The diameter of the cylinder, d = 4.2 cm.The radius of the cylinder, r = d/2

⇒ r = 4.2 ÷ by 2

⇒ r = 2.1 cm

∴ The radius is 2.1 cm

The lateral Surface area of the cylinder = 2πrh

⇒ 2 × π × 2.1 × 12.3

⇒ 51.66 π

We know the default value of π is 3.14

⇒ 51.66 × 3.14

⇒ 162.2 cm²

To find the lateral Surface area of the prism :

The given information are,

The height of the prism, h = 10.3 cm.The three bases of the prism are b1 = 8 cm, b2 = 8 cm, b3 = 6 cm.

The lateral Surface area of the triangular prism = (b1+b2+b3)×h

⇒ (8+8+6) × 10.3

⇒ 22 × 10.3

⇒ 226.6 cm²