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BabaBlast [244]
3 years ago
5

Given that the hypotenuse of this right triangle is 25 cm long and that tan(θ) = 3find the values of x and y, accurate to the ne

arest tenth.
Mathematics
2 answers:
Elanso [62]3 years ago
8 0

Answer:x ≈ 7.9; y ≈ 23.7

Step-by-step explanation:

The right triangle above you can use SOHCAHTOA and determine that tanθ =

y

x

. Replacing tanθ with 3 you get

3 =

y

x

3x = y

Then use the Pythagorean Theorem to

x2 + y2 = 252. Replace y with 3x

x2 + 9x2 = 625

10x2 = 625

x2 =

625

10

x =

25

10

= 7.9

Since,

y = 3x

y = 3(7.9) = 23.7

lara31 [8.8K]3 years ago
4 0
The tangent of an angle is the opposite side divided by the adjacent side of the triangle, relative to the angle. By tan theta = 3, it means that, the adjacent side is thrice as long as the opposite side.

3a = o

Then, using Pythagorean's theorem:

25² = a² + o²
Substituting o,
25² = a² + (3a)²
25² = a² + 9a²
25² = 10a²
a = 7.9 cm

Then, 3(7.9) = o = 23.7 cm

So, the opposite side is 23.7 cm and the adjacent side is 7.9 cm.
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A

The  test statistics is  t  = -1.7

B

The  Null and  Alternative hypothesis are

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Step-by-step explanation:

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     The  sample mean is  \= x  =  47.0

      The sample  standard deviation is  \sigma  =  1.9

      The level of significance is  \alpha  =  0.02

Given that the value which the manufacturer gave the automobile is  47.2 and  it is believed that this is not correct, then  

The  Null Hypothesis is  

        H_o  :  \mu = 47.2

The alternative Hypothesis  is  

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The test statistics can be mathematically evaluated as  

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substituting values

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