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Rina8888 [55]
3 years ago
11

Which of the following functions gives the length of the base edge, a(v), of a right square pyramid that is 8 inches tall as a f

unction of its volume, v, in
cubic inches?
Mathematics
1 answer:
Reil [10]3 years ago
3 0

Answer:

\large\boxed{a(V)=\sqrt{\dfrac{3V}{8}}}

Step-by-step explanation:

The formula of a volume of a square pyramid:

V=\dfrac{1}{3}a^2h

a - base edge

h - height of a pyramid

We have H = 8in.

Substitute and solve for a:

\dfrac{1}{3}a^2(8)=V\\\\\dfrac{8}{3}a^2=V\qquad\text{multiply both sides by}\ \dfrac{3}{8}\\\\\dfrac{3\!\!\!\!\diagup^1}{8\!\!\!\!\diagup_1}\cdot\dfrac{8\!\!\!\!\diagup^1}{3\!\!\!\!\diagup_1}a^2=\dfrac{3}{8}V\\\\a^2=\dfrac{3V}{8}\Rightarrow a=\sqrt{\dfrac{3V}{8}}

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Find the values of the six trigonometric functions for angle G.
EleoNora [17]

Answers:

  • sin(G) = 3/5
  • cos(G) = 4/5
  • tan(G) = 3/4
  • csc(G) = 5/3
  • sec(G) = 5/4
  • cot(G) = 4/3

==============================================

Explanation:

For a right triangle, the sine of a reference angle is equal to the opposite over hypotenuse.

sin(angle) = opposite/hypotenuse

cosine involves adjacent over hypotenuse

cos(angle) = adjacent/hypotenuse

tangent involves opposite over adjacent

tan(angle) = opposite/hypotenuse

-----------------

In short, we have this list so far

  • sin(angle) = opposite/hypotenuse
  • cos(angle) = adjacent/hypotenuse
  • tan(angle) = opposite/hypotenuse

The other three trig functions are reciprocals of these first three. Cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent.

Meaning, the other three trig ratios are

  • csc(angle) = hypotenuse/opposite
  • sec(angle) = hypotenuse/adjacent
  • cot(angle) = adjacent/opposite

--------------------

So,

  • sin(G) = opposite/hypotenuse = FH/FG = 24/40 = 3/5
  • cos(G) = adjacent/hypotenuse = GH/FG = 32/40 = 4/5
  • tan(G) = opposite/adjacent = FH/GH = 24/32 = 3/4

and

  • csc(G) = hypotenuse/opposite = FG/FH = 40/24 = 5/3
  • sec(G) = hypotenuse/adjacent = FG/GH = 40/32 = 5/4
  • cot(G) = adjacent/opposite = GH/FH = 32/24 = 4/3
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∠WZX = 90 - (13 + 20) = 57°

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