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3 years ago

The hypotenuse of a right triangle is 12, and one of the legs is 4. Find the length of the

Mathematics

1 answer:

MAXImum [283]3 years ago

3 0

The length of the missing leg is 11.31

<h3>Pythagorean theorem formula</h3>

a² + b² = c²

<em>While</em><em> </em><em>c</em><em> </em><em>is</em><em> </em><em>the</em><em> </em><em>hypotenu</em><em>se</em><em> </em><em>part</em><em>.</em>

<h3>Known</h3>

a = 4

b = ..?

c = 12

a² + b² = c²

4² + b² = 12²

16 + b² = 144

b² = 144 - 16

b² = 128

b = √128

b = 11.3137085

#nearest hundreth (2 decimal places)

b = 11.31

<h3>Note for moderator who see this</h3>

#Moderators please don't be mean, dont delete my answers just to get approval from your senior or just to get the biggest moderation daily rank.

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Use appropriate identities to rewrite the wave equation shown below in the form ℎ(x) = a cos (x − c).

yarga [219]

Answer:

$h(x) = 10 cos(x-36.870)$

Step-by-step explanation:

Note: For this problem we use the calculator on degrees

For this case we need to remember this identity :

$Cos (a-b) = cos a cos b + sin a sin b$

For this case if we apply for our desired formula we got this:

$a cos (x-c) = a [cos (c) cos (x) + sin (c) sin (x)]$

And we want this equal to $h(x) = 6 sin (x) + 8 cos (x)$ so we can set up the following equality:

$6 sin (x) + 8 cos (x)= a cos (c) [cos (x)] + a sin (c) [sin(x)]$ (1)

If we apply direct comparison between the factors on equation (1) we see this:

$a cos(c) = 8$ (2)

$a sin (c) = 6$ (3)

If we solve a from equation (2) we got:

$a = \frac{8}{cos (c)}$ (4)

If we replace equation (4) into equation (3) we got:

$\frac{8}{sin(c)} cos (c) = 8 tan (c) = 6$

$tan(c) = \frac{6}{8}=\frac{3}{4}$

If we apply inverse tangent on both sides we got:

$c = tan^{-1} (3/4) = 36.870$

So then the value of c= 36.870 degrees. And since w ehave the value of c we can find the value for a and we got:

$[tex] a = \frac{8}{cos (36.870)}=10$

And then our expression in the form $h(x) = a cos (x-c)$ is:

$h(x) = 10 cos(x-36.870)$

And we can check that:

$h(x)= 10 cos (36.870) [cos (x)] + 10 sin (36.870) [sin(x)]= 8 cos (x) + 6 sin (x)$

8 0

3 years ago

To repair a roof that is 12 feet high, Mr. Callahan leans a 13-foot ladder against the side of the building. To reach the roof,

Varvara68 [4.7K]

Answer:

5 feet away

Step-by-step explanation:

It is a Pythagorean Triple.

The hypotenuse is 13 feet and one of the sides is 12 feet. To find the length of the base, use the Pythagorean Theorem.

13^2=12^2+c^2

169=144+c^2

c^=25

c=5

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lozanna [386]

Answer:

Step-by-step explanation:

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1 year ago

1 inch corresponds to 4ft, what is 2 1/4 inches converted to feet

Roman55 [17]

Answer:

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Step-by-step explanation:

2 1/4 can be written as an improper fraction 9/4

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1 inch ----> corresponds to 4 feet

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4 years ago

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Likurg_2 [28]

Answer:

-25/3

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

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