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3 years ago

What is the sine of A as a fraction?

Mathematics

1 answer:

NARA [144]3 years ago

7 0

Answer:

15/17

Step-by-step explanation:

Sine is $\frac{opposite}{hypotenuse}$ , and we see that the angle opposite of A is 15 while the hypotenuse is 17. Plug that into your formula and you get $\frac{15}{17}$ .

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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

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2 years ago

If a basketball player consistently shoots 80% from the free throw line and she takes 25 free throw shots throughout the course

faltersainse [42]

The formula for percentage is:

is/of = %/100

In the given problem,
is = ?
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We get,

?/25 = 80/100

"is" is unknown so let "is" be "x"

x/25 = 80/100

We have to cross multiply. Meaning, we will multiply the numerator of one fraction by the denominator of the other fraction. Therefore,

100x = (80)(25)
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The answer is 20. The basketball player is expected to make 20 free throw shots out of 25 in the entire game.

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