USE SOCRACTIC IT WOULD REALLY HELP WITH THIS QUESTION
you will need to use the law of cosines since this picture does not indicate that this is a right triangle
c^2 = a^2 + b^2 – 2ab cos C,
16^2 = 17^2+8^2 -2*17*8*cosC
256=289-272cosC
-33=-272cosC
33/272 = cosC
cos^-1 (33/272)=C taking the inverse cos
C=83.0 (to the nearest tenth)
b^2 = a^2 + c^2 – 2ac cos B,
8^2 = 17^2 +16^2 -2*17*16cosB
64=289-544cosB
-225=-544cosB
225/544=cosB
cos^(-1) =B
B=65.5
A=180-83-65.6
A=31.4
The area of the base is:
A = root ((s-a) * (s-b) * (s-c) * (s))
Where,
a, b, c: sides of the triangle
s = (a + b + c) / 2
We have then:
s = (9 + 9 + 9) / 2
s = 13.5
A = root ((13.5-9) * (13.5-9) * (13.5-9) * (13.5))
A = 35.07
Then, the surface area of the prism is:
S.A = 2 * A + 9h + 9h + 9h
Where,
h: height of the prism:
Substituting values:
421.2 = 2 * (35.07) + 9h + 9h + 9h
Clearing h:
27h = (421.2 - 2 * (35.07))
h = (421.2 - 2 * (35.07)) / (27)
h = 13
Answer:
the height of the box is:
h = 13 inches
A decimal is 3.5, or 2.4739464. a number and a little bit. basically not a whole number. :)