All categories

3 years ago

Each side of an equilateral triangle measures 9cm. Find the height, h, of the triangle.

2 answers:

4 0

You can make the equilateral triangle into a right triangle by cutting it in half. So, your sides would be 4.5, 9, and x.
Using Pythagorean Theorem, you know that a^2 + b^2 = c^2.

The 'a' would be equal to 9, and 9^2 is equal to 81.

B is equal to 4.5, and 4.5^2 is 20.25.

So, you have the following:

81 + 20.25 = c^2

And that makes 'c' equal to 101.25.
The square root of 101.25 is approximately equal to 10.06.

So now you know the height, 10.06.

lina2011 [118]3 years ago

3 0

I got 7.8 (rounding to the nearest tenth)
i used the smas formula but i got : (4.5*4.5+x^2=9*9)
so, 20.25+x^2=81
then, x^2= 60.75 (i got 60.75 from subtracting 20.25 from 81)
fonal answer: square root both sides

You might be interested in

steve deposits $1250 in an account paying 3.4% annual interest compounded continously. how long will it take for the account bal

Tomtit [17]

Answer:

It will take 27.19 years

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

$A=Pe^{rt}$ , where

A = the future value of the investment, including interest
P = the principal investment amount (the initial amount)
r = the interest rate of interest in decimal
t = the time the money is invested for

∵ Steve deposits $1250 in an account

∴ P = 1250

∵ The account paying 3.4% annual interest compounded continuously

∴ r = 3.4%

- Change it to decimal by dividing it by 100

∴ r = 3.4 ÷ 100 = 0.034

∵ The account balance will reach to $3150.5

∴ A = 3150.5

- Substitute The values of A, P and r in the formula above to find t

∵ $3150.5=1250e^{0.034t}$

- Divide both sides by 1250

∴ $2.5204=e^{0.034t}$

- Insert ㏑ to both sides

∴ $ln(2.5204)=ln[e^{0.034t}]$

- Remember that $ln(e^{n})=n$

∵ $ln(e^{0.034t})=0.034t$

∴ ln(2.5204) = 0.034t

- Divide both sides by 0.034

∴ 27.18875 = t

∴ t ≅ 27.19

It will take 27.19 years

3 0

3 years ago

Definition:A sailboat set a course of N 25° E from a small port along a shoreline that runs north and south. Sometime later the

kicyunya [14]

Answer:

S 75°E

S 55°E

Step-by-step explanation:

Take the law if sines of a triangle:

$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$

Where,

a = 28 miles

B = 25°

b = 12 miles

First solve for A, using the law of sines:

$\frac{a}{sinA} = \frac{b}{sinB}$

$\frac{28}{sinA} = \frac{12}{sin25}$

Cross multiply:

$28 sin25 = 12 sinA$

$11.83 = 12 sinA$

$Sin A = \frac{11.83}{12}$

$Sin A = 0.986$

$A = sin^-^1(0.986)$

$A = 80.44 degrees$

Since A = 80.44° find A supplement, A`:

A` = 180 - 80.44

A` = 99.56°

If A` + B < 180°, find C.

Thus,

A` + B = 99.56 + 25 = 124.56

We can see that A` + B < 180

Find C:

C = 180 - (80.44+25) = 74.56° ≈ 75°

C` = 180 - (99.56+25) = 55.44° ≈ 55°

Rewrite in bearing form:

S 75°E

S 55°E

5 0

3 years ago

What is the length of side x?

Vinil7 [7]

Answer:

x = 3

Step-by-step explanation:

In a 30-60-90 triangle the side between 60 and 90 degree angle is a, the side between 30 and 90 degree angle is a√3, and the hypotenuse is 2*a.

Given that the side that is supposed to be a is currently √3, we know that the missing side x must be:

a√3 (We know that a, in this case, is √3, so substitute)

x = (√3) * (√3)

x = 3

5 0

3 years ago

You want to put $2,500 in a simple interest account.It has a 4% annual interest rate.How long will it take you to earn $200 in i

prohojiy [21]

It will take 2 years.

Year 1 :
4% 2.5k = 2.5k/100 × 4 = $100 in interest

$2.5k + $0.1k = $2.6k

Year 2 :
4% 2.6k = 2.6k/100 × 4 = $104 in interest

$100 + $104 = $204 > $200

There may be a simpler way to solve this using a formula for example, but I just solved this step by step. Please feel free to ask if you have any questions

7 0

3 years ago

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in sec

pashok25 [27]

Answer:

Step-by-step explanation:

in interval ( 0 ; 2)

in interval (2; 4)

in interval (4 ; 6 )

The graph shows that at first the ball rises up ; and then it is seen that it goes down and loses height to zero , from which it can be concluded that the height after 10 seconds remains unchanged and therefore the height of the ball after 16 seconds will be zero

6 0

3 years ago