We can calculate a side of a triangle if the side's opposite angle, another side and its opposite angle are known using the Sine rule:
a/sin(A) = b/sin(B) = c/sin(C)
Answer: 124
Step-by-step explanation:
Answer:
a) 18 in x 18 in x 18 in
b) 
Step-by-step explanation:
a) Let's call 's' the side of the square base and 'h' the height of the solid.
The surface area is given by the equation:
The volume of the solid is given by the equation:
From the volume equation, we have that:
Then, using this value of h in the surface area equation, we have:
To find the side length that gives the minimum surface area, we can find where the derivative of S in relation to s is zero:
The height of the solid is:
b) The minimum surface area is:
Given tan g = 5/12, find cos g:
5
tan g = ———
12
The tangent function is, by definition, the quotient between sine and cosine:
sin g 5
———— = ———
cos g 12
Product of them extremes = product of the means
12 · sin g = 5 · cos g
Square both sides:
(12 · sin g)² = (5 · cos g)²
12² · sin² g = 5² · cos² g
144 · sin² g = 25 · cos² g
But sin² g = 1 – cos² g. Substitute it for sin² g into the equation above, and you have
144 · (1 – cos² g) = 25 · cos² g
Multiply out the brackets, and then isolate cos² g:
144 – 144 · cos² g = 25 · cos² g
144 = 25 · cos² g + 144 · cos² g
144 = 169 · cos² g
Divide both sides by 169:
144
cos² g = ———
169
12²
cos² g = ———
13²
cos² g = (12/13)²
Now, take the square root of both sides:
cos g = ± √(12/13)²
12
cos g = ± ———
13
The sign of cos g depends on which quadrant the angle g lies. As tan g = 5/12, which is positive, then g lies either in the 1st or the 3rd quadrant:
• If g lies in the 1st quadrant, then
5
cos g > 0 ⇒ cos g = ——— ✔
13
• If g lies in the 3rd quadrant, then
5
cos g < 0 ⇒ cos g = – ——— ✔
13
I hope this helps. =)
Tags: <em>trigonometric relation tangent cosine sine tan cos sin trig trigonometry</em>
Answer:
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Step-by-step explanation:
hope it helps
