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2 years ago

A right triangle has side lengths a, b, and c as shown below.

Mathematics

1 answer:

Musya8 [376]2 years ago

4 0

Answer:

$\bold{\sin x = \frac{b}{c}}\bold{\\\cos x = \frac{a}{c}}\bold{\\\tan x = \frac{b}{a}}$

Step-by-step explanation:

Given that

A right triangle has side lengths a, b, and c

Because you did not attached photo of the right triangle so I will assume that:

Side a is the adjacent (A)
Side b is the opposite (O)
Side c is the hypotenuse (H)

(Please have a look at the attached photo)

To solve for the trigonometric functions of x, we need to recall the ratios they represent as shown below.

$\sin x = \frac{O}{H}\\\cos x = \frac{A}{H}\\\tan x = \frac{O}{A}$

EX: the sine of x is equal to the side opposite of angle x over the hypotenuse. Hence, we have the expressions of the trigonometric functions as shown below:

$\bold{\sin x = \frac{b}{c}}\bold{\\\cos x = \frac{a}{c}}\bold{\\\tan x = \frac{b}{a}}$

Hope it will find you well

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A gallon of paint covers 400 square feet. How many square feet will 2 3/8 gallons of paint cover?

Black_prince [1.1K]

1 gal = 400 ft²
2 3/8 gal = ? ft²

to solve, use similar ratios with units gal/ft² and compare

(1)/(400) = (2 3/8)/(x)

*multiply both sides by (x) and divide both sides by (1)/(400), you get:

x = (400)*(2 3/8)/(1) = 400*(2 3/8) = 400*2 + 400*3/8 = 800 + 150 = 950 ft²

<u><em>answer is 950 ft²</em></u>

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2 years ago

1, 32, 243, 1,024, 3,125____ what is the next number in the pattern

rosijanka [135]

Heyya

I think the pattern is (n+1)^5

1=1^5
32 = 2^5
243 = 3^5
1024 = 4^5
3125 =5^5

Then the next number should be 6^5 = 7776
Hope you get it

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2 years ago

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Which of the following values are in the range of the function graphed below?

Elanso [62]

Hello!

The range is all of the y-values of the function. As we can see, the function is at y-values 0, -2,-4 and -6.

Therefore, our answers are 0 ,-2 and -6.

I hope this helps!

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2 years ago

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Each batch of Mrs. Crawley’s Toffee makes 14 pieces of toffee. If sandy needs 8 dozen pieces of toffee, how many batches does sh

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2 years ago

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The center of a hyperbola is (−2,4) , and one vertex is (−2,7) . The slope of one of the asymptotes is 1/2 .

maxonik [38]

Answer:

<h2>The equation is $\frac{(y - 4)^{2} }{9 } - \frac{(x + 2)^{2} }{36 } = 1$ .</h2>

Step-by-step explanation:

The equation of a hyperbola is represented by $\frac{(y - k)^{2} }{b^{2} } - \frac{(x - h)^{2} }{a^{2} } = 1$ , where (h, k) is the center of the hyperbola.

As per the given condition, h = -2 and k = 4.

Thus, the equation becomes $\frac{(y - 4)^{2} }{b^{2} } - \frac{(x + 2)^{2} }{a^{2} } = 1$ .

One vertex is (-2, 7).

Hence, putting x = -2 and y = 7, we get $b^{2} = 9$ .

The slope of the asymptote is $\frac{b}{a}$ .

Hence, $\frac{b^{2} }{a^{2} } = \frac{1}{4} \\a^{2} = 36$ .

Thus, the equation is $\frac{(y - 4)^{2} }{9 } - \frac{(x + 2)^{2} }{36 } = 1$ .

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2 years ago