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2 years ago

Plz answer question in screen shot

Mathematics

1 answer:

liberstina [14]2 years ago

6 0

Answer:

tan theta = 2 sqrt(5) /15

Step-by-step explanation:

sin theta = opp / hypotenuse

sin theta = 2/7

We can use the Pythagorean theorem to find the length of the adjacent side

a^2 + b^2 = c^2

2^2 +adj^2 = 7^2

4 + adj^2 = 49

adj ^2 = 49-4

adj^2 = 45

Taking the square root of each side

adj = sqrt(45) = sqrt(9*5) =sqrt(9) sqrt(5) = 3 sqrt(5)

The tan theta = opp/ adj

tan theta = 2 / 3 sqrt(5)

Multiply by sqrt(5) / sqrt(5)

= 2 sqrt(5) / 3 *5

= 2 sqrt(5) /15

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Simplify the left side of equation so it looks like the right side. cos(x) + sin(x) tan(x) = sec (x)

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Step-by-step explanation:

Consider LHS

$\cos(x) + \sin(x) \tan(x) = \sec(x)$

Apply quotient identies

$\cos(x) + \sin(x) \times \frac{ \sin(x) }{ \cos(x) } = \sec(x)$

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$\cos(x) + \frac{ \sin {}^{2} (x) }{ \cos(x) } = \sec(x)$

Make cos x a fraction with cos x as it denominator.

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2 years ago

What is the volume, in terms of cubic inches, of a cone with a diameter of 8 inches and a height of 10 inches? Use 3.14 for LaTe

Ad libitum [116K]

Answer:

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Step-by-step explanation:

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3 years ago

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The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

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$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

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Expand

$b^2 +b-7b-7=0$

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$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

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$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

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$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

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Answer:

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Step-by-step explanation:

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3 years ago

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