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3 years ago

Find the complement of an angle whose measure is 54 degrees.

Mathematics

2 answers:

Ugo [173]3 years ago

6 0

I hope this helps you

180-54=126

shepuryov [24]3 years ago

4 0

Complementary angles add up to 90 degrees.
So.... 90 - 54 = 36 degrees

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Dominik [7]

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3 years ago

Slope of 1,-7 and -3-4

3241004551 [841]

$\large \mathfrak{Solution : }$

Slope of the given line is :

$\dfrac{y_2 - y_1}{x_2 - x_1}$

where ,

$x_2 = 1$

$x_1 = - 3$

$y_2 = - 7$

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let's solve :

$\dfrac{ - 7 - ( - 4)}{1 - ( - 3)}$

$\dfrac{ - 3}{4}$

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3 years ago

Which value is a solution of the equation 85= 120-w?

Ronch [10]

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3 years ago

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I need to show how to find these solutions 1/4 and 3/4 by completing the square!

Arlecino [84]

Answer:

See explanation, and ask for more details if unclear!

Step-by-step explanation:

The perfect square of this equation is $x^2-x+\frac{1}{4}$ , since the square would be $(x-\frac{1}{2})^2$ . 1/4=4/16, meaning that you can set up the equation in the following way:

$(x^2-x+\frac{1}{4})-\frac{1}{16}=0$

$(x-\frac{1}{2})^2=\frac{1}{16}$

Take the square root of both sides:

$x-\frac{1}{2}=\pm \frac{1}{4}$

Add 1/2 to both sides:

$x=\frac{1}{2}\pm \frac{1}{4}=\frac{3}{4}, \frac{1}{4}$ . Hope this helps!

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3 years ago

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Find the longer leg of the triangle.

Paha777 [63]

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

The length of the hypotenuse (the side opposite to the right angle) is given.
The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let $\text{Opposite}$ denotes the length of the side opposite to the $30^{\circ}$ acute angle, and $\text{Adjacent}$ be the length of the side next to this $30^{\circ}$ acute angle.

$\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}$ .

Similarly,

$\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}$ .

The longer leg in this case is the one adjacent to the $30^{\circ}$ acute angle. The answer will be $3$ .

There's a shortcut to the answer. Notice that $\sin{30^{\circ}} < \cos{30^{\circ}}$ . The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the $30^{\circ}$ angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship $\sin{\theta} < \cos{\theta}$ holds for all acute angles? (That is, $0^{\circ} < \theta$ ?) It turns out that:

$\sin{\theta} < \cos{\theta}$ if $0^{\circ} < \theta$ ;
$\sin{\theta} > \cos{\theta}$ if $45^{\circ} < \theta$ ;
$\sin{\theta} = \cos{\theta}$ if $\theta = 45^{\circ}$ .

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3 years ago

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