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djyliett [7]
3 years ago
5

What is the length of the altitude of the equilateral triangle below

Mathematics
2 answers:
Nastasia [14]3 years ago
8 0
Please mark me as brainliest!
<span>The altitude divides the triangle into a 30-60-90 triangle. So we can use the 30-60-90 Triangle Theorem to find the altitude. which is: hypotenuse= 2 x shorter leg Longer leg = sqrt(3) x shorter leg</span>
kolezko [41]3 years ago
6 0

Method 1

Applying the Pythagorean Theorem

we know that

10^{2}= 5^{2} +a^{2}

Solve for a

100= 25 +a^{2}

a^{2}=100-25

a^{2}=75

a=\sqrt{75}=5 \sqrt{3}\ units

therefore

<u>the answer is</u>

the length of the altitude is 5 \sqrt{3}\ units

Method 2

we know that

sin(60\°)=\frac{\sqrt{3}}{2} -------> equation A

and

in this problem

sin(60\°)=\frac{a}{10} --------> equation B

equate equation A and equation B

\frac{\sqrt{3}}{2}=\frac{a}{10}\\\\a=\frac{10\sqrt{3}}{2}\\\\a=5 \sqrt{3}\ units

therefore

the answer is

the length of the altitude is 5 \sqrt{3}\ units

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Overline MD cong overline LS additional information is necessary to show that triangle MTD cong triangle LGS by SSS?
aivan3 [116]

Answer:

TD \cong GS

Step-by-step explanation:

See comment for complete question

Given:

TM \cong GL

MD \cong LS

Required

The information that shows \triangle MTD \cong \triangle LGS by SSS

By SSS implies that, the three sides of both triangles are congruent

Already, we have:

TM \cong GL

MD \cong LS

The third side of \triangle MTD is TD

The third side of \triangle LGS is GS

So, for both to be congruent by SSS, the third sides must be congruent

i.e.

TD \cong GS

4 0
2 years ago
The table shows a linear function. <br>which equation represents the function?
Bas_tet [7]

Answer:

Option C is correct.

The equation f(x)= -\frac{1}{2}x +4 represents the function.

Step-by-step explanation:

Using slope intercept form to find the equation of line :

For any two points (x_1, y_1) and  (x_2, y_2) the equation of line is given by:

y -y _1 = m(x-x_1) ......[1] ;where m is the slope given by:

m = \frac{y_2-y_1}{x_2-x_1}

Consider any two points from table :

let (4, 2) and (0, 4) be any two points.

calculate slope:

m = \frac{y_2-y_1}{x_2-x_1}= \frac{4-2}{0-4}

m = \frac{2}{-4} = -\frac{1}{2}

Now, substitute in equation [1]  we have:

y - 2 = -\frac{1}{2} (x-4)

Distributive property i.e,  a\cdot (b+c) = a\cdot b + a\cdot c

y -2 = -\frac{1}{2}x +2

Add both sides 2 we get;

y -2+2 = -\frac{1}{2}x+2+2

Simplify:

y = -\frac{1}{2}x+4

Since, y= f(x)

f(x)= -\frac{1}{2}x +4

therefore, the equation f(x)= -\frac{1}{2}x +4 represents the function.


8 0
3 years ago
What’s the work and answer for this? Someone please tell me
Yuliya22 [10]

Answer:

3

Step-by-step explanation:

3 0
2 years ago
Write the equation of the circle whose center is (-5, -8) with diameter 12
lora16 [44]

Answer:

(x + 5)^2 + (y + 8)^2 = 6^2

Step-by-step explanation:

A circle formula: (x - h)^2 + (y - k)^2 = r^2

We are given diameter. To find the radius divide diameter by 2.

d = 12

12/2 = r = 6

H and K are given to be (-5 , -8)

(x - (-5))^2 + (y - (-8))^2 = 6^2

(x + 5)^2 + (y + 8)^2 = 6^2

I have plot this equation to confirm my answer is correct where the origin is (-5 , -8) and has a radius of 6.

3 0
1 year ago
3 x one half<br><br><br> three halves<br><br> five sixths<br><br> one sixth<br><br> one half
fomenos

Answer:

three halves

Step-by-step explanation:

1/2 * 3 = 3/2 = 1 1/2 = 1.5

Multiple: 1/2 * 3 = 1 · 3/2 · 1 = 3/2

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(3, 2) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one half multiplied by three = three halfs.

3 0
1 year ago
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