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4 years ago

Please Help, Will give Brainliest! Law Of Cosines.

Mathematics

1 answer:

stealth61 [152]4 years ago

6 0

Answer:

B) a = 6.7, B = 36°, C = 49°

Step-by-step explanation:

Fill in the numbers in the Law of Cosines formula to find the value of "a".

a² = b² + c² -2bc·cos(A)

a² = 4² +5² -2(4)(5)cos(95°) ≈ 44.4862

a ≈ √44.4862 ≈ 6.66980

Now, the law of sines is used to find one of the remaining angles. The larger angle will be found from ...

sin(C)/c = sin(A)/a

sin(C) = (c/a)sin(A)

C = arcsin(5/6.6698×sin(95°)) ≈ 48.31°

The third angle is ...

B = 180° -A -C = 180° -95° -48.31° = 36.69°

The closest match to a = 6.7, B = 37°, C = 48° is answer choice B.

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3 years ago

What is the range of possible sizes for side x

Xelga [282]

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Step-by-step explanation:

For a triangle (by the triangular inequality theorem), we know that the sum of any two sides must be larger than the other side.

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3 years ago

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andrey2020 [161]

Answer:

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Step-by-step explanation:

You know how subtraction is the opposite of addition and division is the opposite of multiplication? A logarithm is the opposite of an exponent. You know how you can rewrite the equation 3 + 2 = 5 as 5 - 3 = 2, or the equation 3 × 2 = 6 as 6 ÷ 3 = 2? This is really useful when one of those numbers on the left is unknown. 3 + _ = 8 can be rewritten as 8 - 3 = _, 4 × _ = 12 can be rewritten as 12 ÷ 4 = _. We get all our knowns on one side and our unknown by itself on the other, and the rest is computation.

We know that $3^2=9$ ; as a logarithm, the exponent gets moved to its own side of the equation, and we write the equation like this: $\log_3{9}=2$ , which you read as "the logarithm base 3 of 9 is 2." You could also read it as "the power you need to raise 3 to to get 9 is 2."

One historical quirk: because we use the decimal system, it's assumed that an expression like $\log1000$ uses base 10, and you'd interpret it as "What power do I raise 10 to to get 1000?"

The expression $\log100=x$ means "the power you need to raise 10 to to get 100 is x," or, rearranging: "10 to the x is equal to 100," which in symbols is $10^x=100$ .

(If we wanted to, we could also solve this: $10^2=100$ , so $\log100=2$ )

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