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Paha777 [63]
3 years ago
14

Find the measure of Q, the smallest angle in the triangle whose sides have lengths 4-5, and 6. Round the measure to the nearest

whole degree.

Mathematics
1 answer:
kakasveta [241]3 years ago
4 0

<u>Given</u>:

Given that PQR is a triangle.

The measures of the sides of the triangle are 4,5 and 6.

We need to determine the measure of ∠Q.

<u>Measure of ∠Q:</u>

The measure of ∠Q can be determined using the law of cosines formula.

Thus, we have;

\cos (Q)=\frac{p^{2}+r^{2}-q^{2}}{2 p r}

Substituting p = 6, q = 4, r = 5, we get;

\cos (Q)=\frac{6^{2}+5^{2}-4^{2}}{2 (6)(5)}

Simplifying, we get;

\cos (Q)=\frac{36+25-16}{2 (30)}

\cos (Q)=\frac{45}{60}

Dividing, we get;

\cos (Q)=0.75

      Q=cos^{-1}(0.75)

      Q=41^{\circ}

Thus, the measure of ∠Q is 41°

Hence, Option b is the correct answer.

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That's a question about percentage.

One way to represent percentage is using decimal number. In this way, 1 is equivalent to 100% and the other less percentages using numbers between 0 and 1.

Examples:

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  • 13.17% is equivalent to 0.1317.
  • 245% is equivalent to 2.45.

If we want to know the percentage of a number, we should multiplacate the number by the porcentage in the decimal number form.

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  • 55.90% of 200 is equal to: 200 \times 0.5590 = 111.8
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In our problem, we have a phone with a increase of 7%. To solve that, it's important to perceive that $230 is equal to 100% and with a increase of 7%, we will pay 107%.

107% in the decimal number form is 1.07. With that information, we should multiplicate 1.07 by the original value and we will find the answer.

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I hope I've helped. :D

Enjoy your studies. \o/

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