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3 years ago

Find the value of x round to the nearest tenth, i'm good with all other trigonometry lol

Mathematics

1 answer:

liraira [26]3 years ago

6 0

Answer:

8.4 cm

Step-by-step explanation:

The sides involved are opposite and adjacent to the given angle. Therefore, you should use the tangent ratio.

Substitute:

tanx = opp/adj

tan35 = x/12

Multiply by 12 on both sides:

12(tan35) = (x/12)12

12(tan35) = x

Solve:

12(tan35) = x

8.4 = x

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What is the factored form of 64g^3 +8?<br>

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3 years ago

The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.

MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle = $3\times\ side$

$3\times\ side$ $=[tex]81\sqrt{3}$

$Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm$

Thus from the diagram , Side $AB=BC=AC= 27\sqrt{3} \ cm$

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus $\angle OBC = 30$ °

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

$tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2} } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\$

Thus ,apothem OE= 13.5 cm

Now for radius,

We consider ΔOBE

$cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB} \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm$

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

4 0

3 years ago

What is 4 to the power of x minus 3 =18

mote1985 [20]

3 to the power of 4:

=34
x
n
=
3
4

=3⋅3⋅3⋅3
=
3
⋅
3
⋅
3
⋅
3

=81
=
81

For example, 3 to the power of -4:

=3−4
x
n
=
3
−
4

=134
=
1
3
4

=13⋅3⋅3⋅3
=
1
3
⋅
3
⋅
3
⋅
3

=181
=
1
81

=0.012346

7 0

3 years ago