Answer:
cos(θ) = (√33)/7
Step-by-step explanation:
The relevant relation is ...
cos(θ) = √(1 -sin²(θ))
cos(θ) = √(1 -(4/7)²) = √(1 -16/49) = √(33/49)
cos(θ) = (√33)/7
Given:
Net of a triangular prism
To find:
Which equation can be used to calculate the surface area of the triangular prism.
Solution:
Using formulas:
Area of rectangle = length × width
Area of triangle = ![\frac{1}{2}\times b\times h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20b%5Ctimes%20h)
Area of left triangle = ![\frac{1}{2}\times 5\times 12](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ctimes%205%5Ctimes%2012)
Area of right triangle = ![\frac{1}{2}\times 5\times 12](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ctimes%205%5Ctimes%2012)
Area of bottom = 5 × 10
Area of Middle = 12 × 10
Area of top = 13 × 10
Surface area of triangular prism:
Surface area = Area of left triangle + Area of right triangle + Area of bottom + Area of middle + Area of top
![$=\frac{1}{2}\times 5\times 10+\frac{1}{2}\times 5\times 10+5\times 10+12\times 10+13\times 10](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%205%5Ctimes%2010%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%205%5Ctimes%2010%2B5%5Ctimes%2010%2B12%5Ctimes%2010%2B13%5Ctimes%2010)
Replace multiplication by brackets.
![$=\frac{1}{2}(5)(10)+\frac{1}{2}(5)(10)+5( 10)+12( 10)+13( 10)](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B2%7D%285%29%2810%29%2B%5Cfrac%7B1%7D%7B2%7D%285%29%2810%29%2B5%28%2010%29%2B12%28%2010%29%2B13%28%2010%29)
The equation can be used to calculate surface area of triangular prism is
.
(6x9)/2=27..........................
U divide the shapes into two, you get a square and triangle. to find area you do b•h, so, 9•6=54,,, now u find area for the triangle wish is b•h/2,, 6•3/2= 9,,, the total area is 54+9=63
Just plug and chug :)
h(-29)=-1/2(-29)+3
h(-29)=29/2+3
h(-29)=-11.5