In ΔSTU, u = 84 inches, s = 13 inches and ∠T=165°. Find the length of t, to the nearest inch.

Answers

Answer 1

Answer:

97

Step-by-step explanation:

I used the law of cosines:  [tex]t^{2} =s^{2} +u^{2} -2tu cos (t)[/tex]

Let plug the numbers in :  t^2=[tex]13^{2} +84^{2} -2(13)(84)cos (165)[/tex] which approx is 97 to the nearest inch.

Answer 2

The length of 't' is approximately 69 inches.

How to calculate the length?

To find the length of t, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:

a²= b² + c² - 2bc cos(A)

In this case, we want to find the length of t, which is opposite to the given angle ∠T. We know that:

u = 84 inches (opposite to angle ∠U)

s = 13 inches (opposite to angle ∠S)

∠T = 165°

Let's substitute these values into the Law of Cosines:

t² = u²+ s²- 2us cos(T)

t²= (84)²+ (13)² - 2(84)(13) cos(165°)

t²= 7,056 + 169 - 2(84)(13)(cos(180°-15°))

t²= 7,225 - 2(84)(13)(cos(15°))

t²= 7,225 - 2(84)(13)(0.9659)

t²= 7,225 - 2,485.68

t² = 4,739.32

t ≈ 68.86

Rounding to the nearest inch, the length of t is approximately 69 inches.

To know more about the law of cosines follow

https://brainly.com/question/13098194

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Step-by-step explanation:

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x    37

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