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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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The given value is 2/3, so the opposite would just mean you flip the numerator and denominator. Thus, the reciprocal of 2/3 is 3/2.

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3 0
2 years ago
Samuel and Christopher go to the movie theater and purchase refreshments for their friends. Samuel spends a total of $34.00 on 6
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Answer:

The system of equations is :

6 p + 4 d = 34

12 p + 7 d = 66.25

The price of a drink is $1.75

Step-by-step explanation:

Assume that the price of one bag of popcorn is $p and the price of a drink is $d

∵ Samuel spends a total of $34 on 6 bags of popcorn and

   4 drinks

- Multiply p by 6 and d by 4, then add the products and equate

    the sum by 34

∴ 6 p + 4 d = 34 ⇒ (1)

∵ Christopher spends a total of $66.25 on 12 bags of popcorn

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- Multiply p by 12 and d by 7, then add the products and equate

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The system of equations is :

6 p + 4 d = 34

12 p + 7 d = 66.25

Now let us solve it

Multiply equation (1) by -2 to make the coefficients of p in the two equations equal in values and opposite in signs to eliminate it

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- Add equations (2) and (3)

∴ - d = - 1.75

- Divide both sides by -1

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