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2 years ago

Find the value of x. Round to the nearest tenth.

Mathematics

1 answer:

neonofarm [45]2 years ago

6 0

Answer:

x ≈ 13.7

Step-by-step explanation:

Using the sine ratio in the white right triangle

sin17° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{47}$

Multiply both sides by 47

47 × sin17° = x, thus

x ≈ 13.7 ( to the nearest tenth )

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Fofino [41]

Answer:

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Step-by-step explanation:

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2 years ago

I need help!! please, you don’t even have to do it all just explain to me how to do the first one I’ll catch on

lisov135 [29]

Hi there!

What we need to know:

The three main trigonometric ratios are sine, cosine and tangent:

$\displaystyle sin\theta=\frac{opposite}{hypotenuse}$ $\displaystyle cos\theta=\frac{adjacent}{hypotenuse}$ $\displaystyle tan\theta=\frac{opposite}{adjacent}$

"Opposite" refers to the side opposite the angle that is not the hypotenuse.

"Hypotenuse" refers to the side opposite the right angle of a right triangle.

"Adjacent" refers to the side next to the angle that is not the hypotenuse.

"θ" is read as "theta". It just represents the angle.

Keep in mind that these three ratios only apply to right triangles.

You can use the mnemonic "soh-cah-toa" to help you remember these ratios.

First question

For the first question, we're given the angle with a measure of 56 degrees and the length of the hypotenuse. We must calculate a, which represents the side adjacent to the given angle.

Given the hypotenuse and the adjacent side, we know that we must use the cosine ratio:

$\displaystyle cos\theta=\frac{adjacent}{hypotenuse}$

Plug in the given information:

$\displaystyle cos56=\frac{a}{13}$

Isolate a by multiplying both sides by 13:

$13\displaystyle cos56=a$

Solve using a calculator:

$a=7.3$

Therefore, a is equal to 7.3 when rounded to 1 decimal place.

Other information you will need to know:

In the above question, we needed to solve for a side. But what if we were given two sides and we needed to solve for an angle? For example:

$\displaystyle sin\theta=\frac{5}{8}$

In this case, we will use the inverse sine ratio:

$\displaystyle \theta=sin^-^1(\frac{5}{8})$

Solve using a calculator:

$\displaystyle \theta=39$

Therefore, the angle would equal approximately 39 degrees.

I hope this helps!

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2 years ago

The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 16 years; the

STatiana [176]

Using the Emperical rule:

68% lie with one one standard deviation:

16 + 1.7 , 16-1.7 = 17.7, 14.3

14.3 is part of the 68%.

The remaining 32% of the distribution is outside the range, with half being less than and half being greater than.

32/2 = 16

The probability of living loner than 14.3 Would be 16%

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2 years ago

Find the slope intercept form of an equation given its slope is 1/4 and y intercept is - 3/4

MA_775_DIABLO [31]

Answer:

y=1/4x-3/4

Step-by-step explanation:

y=mx+b

m=1/4

b=-3/4

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2 years ago

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AveGali [126]

Step-by-step explanation:

remember, tan = sin/cos.

of course, one solution is x = 0. sin(0) = 0, tan(0)=0).

for the general solution we look at x <> 0.

3×sin(x) = 2×tan(x) = 2×sin(x)/cos(x)

3 = 2/cos(x)

3×cos(x) = 2

cos(x) = 2/3

x = 48.1896851...°

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1 year ago