All categories

3 years ago

What is the height of an equilateral triangle if the sides are 10

Mathematics

1 answer:

4vir4ik [10]3 years ago

7 0

Answer:

The height of the equilateral triangle is $5\sqrt{3}\ units$

Step-by-step explanation:

we know that

An equilateral triangle has three congruent sides, and three congruent angles that each measure 60 degrees

To find out the height of an equilateral triangle, apply the Pythagoras Theorem in the right triangle ABD

Remember that the height of an equilateral triangle bisects the base.

see the attached figure to better understand the problem

$AB^2=AD^2+BD^2$

substitute the given values

$10^2=5^2+BD^2$

Solve for BD

$100=25+BD^2$

$BD^2=100-25$

$BD^2=75$

$BD=\sqrt{75}\ units$

simplify

$BD=5\sqrt{3}\ units$ `

therefore

The height of the equilateral triangle is $5\sqrt{3}\ units$

You might be interested in

A study of 420 comma 000 cell phone users found that 134 of them developed cancer of the brain or nervous system. Prior to this

Vesnalui [34]

Answer: (0.00306,0.00334)

Step-by-step explanation:

Given : Sample size : n= 420000

The number of users developed cancer of the brain or nervous system =134

Then , the proportion of users developed cancer of the brain or nervous system :

$p=\dfrac{134}{420000}\approx0.0032$

Significance level : $1-0.90=0.1$

Critical value : $z_{\alpha/2}=1.645$

The confidence interval for population proportion is given by :-

$p\ \pm\ z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}\\\\=0.0032\pm (1.645)\sqrt{\dfrac{(0.0032)(1-0.0032)}{420000}}\approx0.0032\pm0.00014\\\\=(0.00306,0.00334)$

Hence, the 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system is (0.00306,0.00334).

4 0

3 years ago

47:47

BARSIC [14]

Sorry, I'm not sure.

I would suggest asking a trusted adult or teacher or redoing the lesson. Cheating isn't a good path: you will not do well in the future if you always search for answers on the internet.

3 0

1 year ago

The gear is one of the oldest mechanical devices. It has been used since ancient times for its ability to increase or decrease r

eduard

The large gear attached to the pedals connected to the smaller gear

attached to the wheel allows the bicycle to travel further per rotation.

Correct responses:

Part A: Approximately 10.47 inches

Part B: 300°The d

Part C: Approximately 125.66 inches

Part D: The distance traveled increases by approximately 62.83 inches

<h3 /><h3>Methods used to calculate the above values</h3>

Given:

The radius of the large central gear, <em>r</em> = 4 inches

Radius of the small gear = 2 inches

Part A:

The distance travelled by the larger gear when the angle of rotation is 150° is given as follows;

$\displaystyle Distance \ travelled \ by \ larger \ gear = \mathbf{\frac{150^{\circ}}{360^{\circ}} \times 2 \times \pi \times 4 \, inches} = \frac{10}{3} \cdot \pi \ inches$