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1 year ago

The triangle below is equilateral. Find the length of side xx in simplest radical form with a rational denominator.

Mathematics

1 answer:

mylen [45]1 year ago

6 0

The length of side x in simplest radical form with a rational denominator is 8√3

<h3>How to find the length of side x in simplest radical form with a rational denominator?</h3>

The given parameters are:

Triangle type = Equilateral triangle

Height (h) = 12

Missing side length = x

The missing side length, x is calculated using the following sine ratio

sin(60) = Height/Missing side length

This gives

sin(60) = 12/x

Make x the subject of the formula

So, we have

x = 12/sin(60)

Evaluate the quotient

So, we have

x = 12/(√3/2)

This gives

x = 24/√3

Rationalize

x = 24/√3 * √3/√3

Evaluate

x = 8√3

Hence, the length of side x in simplest radical form with a rational denominator is 8√3

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What is the length of the apothem of a regular hexagon with 10-cm sides?

vodka [1.7K]

Answer:

The length of apothem of given hexagon is 8.66 cm

Step-by-step explanation:

Apothem of a polygon is given by:

$apothem = \frac{s}{2\ tan\ (\frac{180}{n})}$

Here

s is length of side

tan is trigonometric function

and n denotes number of sides

Given that the polygon is a hexagon

$s = 10cm\\n = 6$

Putting the values in the formula

$apothem = \frac{10}{2\ tan\ (\frac{180}{6})}\\= \frac{10}{2\ tan\ 30}\\=\frac{10}{2 * 0.5773}\\=\frac{10}{1.1546}\\=8.6610\\Rounding\ off\ to\ nearest\ hundredth\\= 8.66\ cm$

Hence,

The length of apothem of given hexagon is 8.66 cm

6 0

2 years ago

What is the rational number equivalent to 3.12

jekas [21]

Answer:

3 4/33

Step-by-step explanation:

3 0

2 years ago

An umbrella has 12 evenly spaced ribs. If viewed as a flat circle of radius 11 units,

erica [24]

Answer:

Area = 121pi/12

~= 31.66 sq units

Step-by-step explanation:

They are talking about looking at an umbrella like its a circle. The radius is 11 units. That is from the center to the edge.

Consecutive means "in a row" or "next to each other" The 12 "ribs" are the like skeleton structure in the umbrella. But they cut the umbrella into 12 areas. They are asking for the area of one "slice". It is 1/12 of the area of the whole circle.

Area of a circle is

A = pi × r^2

Area of one slice is 1/12 of the whole.

A(1 slice)

= 1/12× pi × r^2

See image.

4 0

2 years ago

Lezlie hiked 3/8 of a mile on Monday. On Wednesday she hiked 3/6 of a mile. She hiked 3/4 of a mile on Friday. Use benchmark num

Gnoma [55]

She walked the most on Friday because you have to find the LCD. The LCD is 24.
For example, to change the denominator of 4 to 24, you must divide 24 divided by 4 which equals 6. Since your answer was 6, you have to multiply both numbers, which are 3 and 4, by 6.
So, 4 times 6 is 24. This is the denominator and 4 times 3 is 18. This is the numerator.
If you do the same with all of the fractions then you will have the fractions of, 18 over 24, 12 over 24, and 9 over 24.
Look at all the numerators (the number on top of the fraction) and decide which one is the biggest.
18 is the biggest and since the fraction 18 over 24 was originally 3 over 4, this means that she walked the most on Friday.
Hoped this helps!!

3 0

3 years ago

What is the solution f/4 = 12/5

Ede4ka [16]

Answer:

f = 48/5

Step-by-step explanation:

5f = 12 * 4

5f = 48

f = 48/5

7 0

2 years ago