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notka56 [123]
3 years ago
15

Suppose a triangle has two sides of length 14 and 14, and that the angle between these two sides is 122 degrees. What is the len

gth of the third side of the triangle?
A. 12.43
B. 18
C. 24.49
D. 22.27

Mathematics
2 answers:
Dafna1 [17]3 years ago
5 0

Suppose we have a triangle ΔABC,

Length of AB = 14

Length of AC = 14

Angle ∠BAC = 122 degree

This triangle is isosceles triangle so, angle B = angle C = (180 - 122)/2 = 29

We know the two side and one angle of triangle ABC, here we use Sine Rule.

(In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.)

According to the law,

\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}

\frac{a}{sinA} =\frac{14}{sin29}

Solve for a

a = 24.49 option C

Schach [20]3 years ago
5 0

We may use the Law of Cosines, among other methods,

c^2 = a^2 + b^2 - 2 ab \cos C = 14^2 + 14^2 - 2(14)(14)\cos 122^\circ

c = \sqrt{14^2 (2 - 2 \cos 122^\circ)} = 14 \sqrt{2 - 2 \cos 122} \approx 24.48935

Choice C

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Answer:

3 gallons

Step-by-step explanation:

Length of the rectangular wall = 23.6 feet

Width of the rectangular wall = 19.2 feet

Surface area of the wall = 23.6 × 19.2

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∴ 1 square feet of the wall will be covered by the amount of paint = \frac{1}{200} gallons

∴ 453.12 square feet will require the amount of paint = \frac{453.12}{200}

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Answer:

She can cut 24 ribbon from this long strip.

Step-by-step explanation:

Given that,

Bella needs identical strips of ribbon measuring 3.5 feet each.

She has 85 feet of ribbon.

3.5 feet is length of 1 ribbon.

1    feet is length of \frac{1}{3.5} ribbon

85 feet is length of \frac{1\times 85}{3.5} ribbon

                              ≈24.28

\frac{85}{3.5}=\frac{85\times10}{35}=\frac{85\times2}{7}=\frac{170}{7}

7) 170(24

   14

_______

     30

     28

  ______

        2

So, she can cut 24 ribbon from this long strip.

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A card is drawn from a well-shuffled deck of 52 cards. What is the probability of getting a red 10?
ohaa [14]

Answer:

1/13

Step-by-step explanation:

<em>Knowing that:</em>

<em>In a deck of card half of the deck of card are red: 1/2  </em>

<em>Also means 52/2 = 26</em>

<em> There are 2 red 10 in a deck of card.</em>

<em>Solve:</em>

<em>Since there are 2 red 10 in a deck of card and half of the deck of 52 card are red also known as 26.</em>

<em>Thus, the probability of getting a red 10 is 2/26. As you can see that not a answer choice. That because 2/26 is a even number as well as it means that it can be simplify.</em>

<em> GCD (or HCF) of 2 and 26 is 2.</em>

<em>Therefore, divide both by 2.</em>

<em>2/2 = 1</em>

<em>26/2 = 13</em>

<em>Hence, we can see that the simplify form is 1/13.</em>

<em>As a result, the probability of getting a red 10 is 1/13.</em>

<em />

<u><em>~lenvy~</em></u>

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