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4 years ago

What is tan C ?

Mathematics

1 answer:

MatroZZZ [7]4 years ago

8 0

Answer:

$\frac{1}{2}$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC of the figure, the tangent of angle C is equal to divide the opposite side to angle C (side AB) by the adjacent side to angle C (side BC)

$tan(C)=\frac{AB}{BC}$

substitute the given values

$tan(C)=\frac{11}{22}$

simplify

$tan(C)=\frac{1}{2}$

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o-na [289]

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4 years ago

What is the volume of a pyramid whose base is a square of area 36 and whose four faces are equilateral triangles?

irina1246 [14]

Answer:

$V = 36\sqrt{2}$

Step-by-step explanation:

The volume of a pyramid is

$V = \dfrac{1}{3}Bh$

where B = area of the base, and h = height of the pyramid

The base is a square.

$A = s^2$

$s = \sqrt{A}$

$s = \sqrt{36}$

$s = 6$

The side of the base has length 6. Each face of the pyramid is an equilateral triangle with side of length 6.

An altitude of this triangle measures

$a = \sqrt{6^2 - 3^2}$

$a = \sqrt{27}$

The pyramid is formed by 4 equilateral triangles whose bases form a square. The tips of the faces meet at a single point on top. The vertical distance from that point to the center of the base is the height of the pyramid.

$h = \sqrt{(\sqrt{27})^2 - 3^2 }$