Respuesta :

The approximate value for t is 5.54

Answer: Option B

Step-by-step explanation:

The law of cosines generalizes the Pythagorean formula to all triangles. It says that [tex]c^{2}[/tex], the square of one side of the triangle, is equal to [tex]a^{2}+b^{2}[/tex] product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.

                      [tex]c^{2}=a^{2}+b^{2}-2 a b \cos C[/tex]

According to the given triangle in figure, the values are

a = 5

b = 4

c = t

[tex]\cos C=\cos 75^{\circ}=0.2588[/tex]

Substituting all the given values in the formula, we get

          [tex]t^{2}=5^{2}+4-(2 \times 5 \times 4 \times 0.2588)[/tex]

          [tex]t^{2}=25+16-10.3527[/tex]

          [tex]t^{2}=41-10.3527=30.647[/tex]

Taking square roots, we get the value for ‘t’ as below,

                             [tex]t=\sqrt{30.647}[/tex]

                             t = 5.536 (approximately 5.54)

brycelaw318

Answer:

B. 5.54

Step-by-step explanation:

To find out what t is, use the formula t=√[r² + s² - 2rs * cos(T)].

t = √[4² + 5² - 2(4(5)) * cos(75)]

t = √[16 + 25 - 8(5) * cos(75)]

t = √[41 - 40 * cos(75)] (For convenience, 40 * cos(75) has been approximated.

t = √[41 - 10]

t = √31

To approximate a square root subtract the lower square (25) from 31 and put that over the higher square (36) minus the lower square (25).

t ≈ 5 + (31 - 25)/(36 - 25)

t ≈ 5 + 6/11

t ≈ 5 6/11 ≈ 5.54, so B is the answer.

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