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3 years ago

Solve the right triangle ABC with right angle C if B=30 degrees and c=10.

2 answers:

4 0

<span>aâ‰8.6602, b=5, A=60 degrees Let's calculate the lengths of the sides and angles and see what option fits. Since the sum of the angles in a triangle equals 180 and we known 2 of the angles, let's calculate angle A first. A = 180 - 90 - 30 = 60 Now for side b. This is a 30/60/90 triangle. The side opposite B is half the length of c since if you were to reflect the triangle across side a, you would have an equilateral triangle. So b is 10/2 = 5. And finally, since we have a right triangle, we can use the Pythagorean theorem to get the remaining side a. So a = sqrt(10^2 - 5^2) = sqrt(100 - 25) = sqrt(75) = 5*sqrt(3) â‰ 8.660254038 And of the available choices, only the last one matches which is aâ‰8.6602, b=5, A=60 degrees As a side note, the last option comes close, but isn't entirely correct since the properly rounded value for a should be 8.6603, not 8.6602.</span>

kenny6666 [7]3 years ago

3 0

C=10, C=90°, B=30°, A+B+C=180°
A+30°+90°=180°⇒A=60°

cos30°=a/c
cos30°=a/10⇒a=cos30°*10
a<span>≃8.6602

c²=a²+b²⇒b²=c²-a²
b²=10²-8.6602²⇒b²=25
b=5
</span>

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Chapman’s brickyard sells bricks and blocks. A brick costs $0.38 and a block costs $1.56. The brickyard filled a $24.80 order, w

Lisa [10]

Answer:

number of bricks = 16 and number of blocks = 12

Step-by-step explanation:

From given information it seems , we need to determine number of bricks and number of blocks.

lets assume number of bricks = x

and number of blocks = y

since total items in brickyard is 28

⇒ number of bricks + number of blocks = 28

⇒ x + y = 28 ----------------------- equation 1

Given that cost of 1 brick = $0.38 and cost of 1 block =$1.56

so cost of x bricks = cost of 1 brick × x = 0.38x

And cost of y blocks = cost of 1 block × y = 1.56y

total cost of 28 items order = $24.80

total cost of 28 items = cost of x bricks + cost of y blocks

⇒0.38x + 1.56y = 24.80 ----------------equation 2

Now we are having following two equations

x + y = 28 ----------------------- equation 1

0.38x + 1.56y = 24.80 ----------------equation 2

from equation 1 we get x = 28 - y , substituting this value of x in equation 2 we get

0.38(28 - y) + 1.56y = 24.80

⇒10.64-0.38y+1.56y= 24.80

⇒1.18y = 24.80 - 10.64

⇒y = 14.16÷1.18 = 12

substituting value of y in equation 1 we get

x + 12 = 28

⇒x = 16

hence number of bricks = x = 16 and number of blocks = y = 12

4 0

3 years ago

What is the area of this triangle ?

oee [108]

Answer:

Area of triangle is 9.88 units^2

Step-by-step explanation:

We need to find the area of triangle

Given E(5,1), F(0,4), D(0,8)

We will use formula:

$Area\,\,of\,\,triangle =\sqrt{s(s-a)(s-b)s-c)} \\where\,\, s = \frac{a+b+c}{2}$

We need to find the lengths of side DE, EF and FD

Length of side DE = a = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side DE = a = $=\sqrt{(5-0)^2+(1-8)^2}\\=\sqrt{(5)^2+(-7)^2}\\=\sqrt{25+49}\\=\sqrt{74}\\=8.60$

Length of side EF = b = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side EF = b = $=\sqrt{(0-5)^2+(4-1)^2}\\=\sqrt{(-5)^2+(3)^2}\\=\sqrt{25+9}\\=\sqrt{34}\\=5.8$

Length of side FD = c = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side FD = c = $=\sqrt{(0-0)^2+(8-4)^2}\\=\sqrt{(0)^2+(4)^2}\\=\sqrt{0+16}\\=\sqrt{16}\\=4$

so, a= 8.60, b= 5.8 and c = 4

s = a+b+c/2

s= 8.6+5.8+4/2

s= 9.2

Area of triangle= $=\sqrt{s(s-a)(s-b)s-c)}\\=\sqrt{9.2(9.2-8.6)(9.2-5.8)(9.2-4)}\\=\sqrt{9.2(0.6)(3.4)(5.2)}\\=\sqrt{97.5936}\\=9.88$

So, area of triangle is 9.88 units^2

4 0

3 years ago

What is 0.000 002 in standard form

Vsevolod [243]

Answer:

$0.000 002 = 2 \times {10}^{ - 6}$

Step-by-step explanation:

It is already in standard form and can be expressed in scientific form as:

$0.000 002 = 2 \times {10}^{ - 6}$

5 0

3 years ago

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Leah walks to soccer practice on Saturday. She leaves her home and walks 600 meters north. Leah then turns east and continues on

Diano4ka-milaya [45]

Answer:

800m

Step-by-step explanation:

this would be solved using Pythagoras theorem

we are to find the base

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c = hypotenuse

600² + b² = 100²

b² = 10000 - 3600

b² = 6400

take the square root of both sides

b = 800m

4 0

2 years ago

The arrivals of clients at a service firm in Santa Clara is a random variable from Poisson distribution with rate 2 arrivals per

ICE Princess25 [194]

Answer:

1.76% probability that in one hour more than 5 clients arrive

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

The arrivals of clients at a service firm in Santa Clara is a random variable from Poisson distribution with rate 2 arrivals per hour.

This means that $\mu = 2$

What is the probability that in one hour more than 5 clients arrive

Either 5 or less clients arrive, or more than 5 do. The sum of the probabilities of these events is decimal 1. So

$P(X \leq 5) + P(X > 5) = 1$

We want P(X > 5). So

$P(X > 5) = 1 - P(X \leq 5)$

In which

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353$

$P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707$

$P(X = 2) = \frac{e^{-2}*2^{2}}{(2)!} = 0.2707$

$P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1804$

$P(X = 4) = \frac{e^{-2}*2^{4}}{(4)!} = 0.0902$

$P(X = 5) = \frac{e^{-2}*2^{5}}{(5)!} = 0.0361$

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.1353 + 0.2702 + 0.2702 + 0.1804 + 0.0902 + 0.0361 = 0.9824$

$P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9824 = 0.0176$

1.76% probability that in one hour more than 5 clients arrive

8 0

2 years ago

Read 2 more answers