All categories

3 years ago

In aΔABC, if ∠B = 60° and the ratio of two sides is a : c = 2 : √3 + 1, then ∠A= ____.

Mathematics

1 answer:

UkoKoshka [18]3 years ago

4 0

Answer:

∠A= 45°....

Step-by-step explanation:

To find ∠A first we have to find the length of side B by cosine law:

b^2 = a^2 + c^2 – 2 a c cos B

b^2=(2)^2 +(√3 + 1)^2 - 2(2)(√3 + 1) cos 60

b^2 = 6

Taking square root at both sides:

√b^2 = √6

b= 2.45

Now we can calculate ∠A by sine law:

b / sin B = a / sin A

2.45 / sin 60 = 2 / sin A

sin A= 2* √3/2 /2.45

sin A = 2√3/2 * 1/2.45

sinA = 2√3/ 4.9

sin A = 0.7069

sin A = 0.707

A=45°

Thus ∠A= 45°....

You might be interested in

I need help ASAP<br> please and thank you

raketka [301]

Answer:if this don't help you sry

Step-by-step explanation:

5 0

3 years ago

1+4=5 2+5=12 3+6=21 8+11=?

g100num [7]

I think the pattern is that you multiply the first number by the second , then add the first number. SO:
e.g. for the first one 1 x 4 = 4 , 4 + 1 = 5
for the second one 2 x 5 = 10, 10 + 2 = 12...
So for 8+11:
you do 8 x 11 = 88 , 88 + 8 = 96

7 0

3 years ago

Suppose that prices of recently sold homes in one neighborhood have a mean of $215,000 with a standard deviation of $8900. Using

bonufazy [111]

Answer:

The minimum percentage of recently sold homes with prices between $197,200 and $232,800 is 75%.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by $100(1 - \frac{1}{k^{2}})$ .

In this question:

Mean of $215,000, standard deviation of $8900.

What is the minimum percentage of recently sold homes with prices between $197,200 and $232,800?

215000 - 2*8900 = 197200

215000 + 2*8900 = 232800

Within 2 standard deviations of the mean, so:

The minimum percentage of recently sold homes with prices between $197,200 and $232,800 is 75%.

4 0

3 years ago

After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil ide

dimaraw [331]

Answer:

The revised probabilities are;

The probability of finding soil with oil = 0.8

The probability of finding soil with good oil = 0.16

The probability of finding medium quality oil = 0.64

Step-by-step explanation:

The given probability of finding soil with high quality oil, P(QO) = 0.20

The probability of finding soil with medium-quality oil, P(OM) = 0.80

The probability of finding soil with no oil, P(ON) = 0.2

Therefore, given that the probability of finding soil with no oil = 0.2, we have;

The probability of finding soil with oil, P(OP) = 1 - the probability of finding soil with no oil

P(OP) = 1 - 0.2 = 0.8

Which gives;

The probability, P(FG) of finding soil with oil and that the oil is good is given as follows;

P(FG) = P(QO) × P(OP) = 0.2 × 0.8 = 0.16

The probability of finding good oil = 0.16

Similarly;

The probability of finding medium quality oil P(FM) = P(OM) × P(OP) = 0.8 × 0.8 = 0.64

Which gives the revised probability as follows;

The probability of finding soil with oil, P(OP) = 0.8

The probability of finding soil with good oil, P(FG) = 0.16

The probability of finding medium quality oil, P(FM) = 0.64.

3 0

3 years ago

Plz answer ASAP! I’ll mark Brainiest. For the right triangles below, find the exact values of the side lengths d and h. If neces

mylen [45]

Answer: d= radical 128

h= 3.46

Step-by-step explanation:

d: pythagorean theorem (8^2+8^2=c^2)

h: tan30= x/6

4 0

3 years ago