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2 years ago

PLEASE HELP ME IT'S DUE TODAY AND IT COULD HELP MY GRADE A LOT

Mathematics

1 answer:

ElenaW [278]2 years ago

8 0

Answer:

c = 13

m∡A = 60°

m∡B = 30°

Step-by-step explanation:

This is a 5-12-13 triangle. However, to make sure, I will put the steps.

Allow for each sides to be denoted as a-b-c, in which c is the hypotenuse (longest side). Set the equation:

a² + b² = c²

Plug in the corresponding numbers to the corresponding variables:

5² + 12² = c²

Simplify. First, solve the exponents, and then add:

(5²) = 5 * 5 = 25

(12²) = 12 * 12 = 144

25 + 144 = c²

c² = 169

Note the equal sign, what you do to one side, you do to the other. Isolate the variable, c, by rooting both sides:

√c² = √169

c = √169 = √(13 * 13) = 13

c = 13

13 is your answer for c.

Note the measurements of the angles. We know that this is a 30-60-90 triangle, and so it will be easy to figure it out. Note that the corresponding angles will depend on that of the opposite side's measurement lengths. The hypotenuse will always be on the opposite side of the largest angle (as given), as c, the longest side, is opposite of ∡C, which is the largest angle (90°). Based on this information, it means that ∡A would be 60° (as it is opposite of the middle number, 12), and ∡B would be 30° (opposite of the smallest number, 5).

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Evaluate the six trigonometric functions of the angle 0.

Arturiano [62]

Given:

Right triangle

To find:

The six trigonometric functions of θ

Solution:

Hypotenuse = 18

Adjacent side to θ = 10

Opposite side to θ = ?

Using Pythagoras theorem:

$\text {Hypotenuse}^2 = \text{adjacent}^2+\text{opposite}^2$

$18^2 =10^2+\text{opposite}^2$

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Subtract 100 from both sides.

$224=\text{opposite}^2$

Taking square root on both sides.

$4\sqrt{14}=\text{opposite}$

Using trigonometric ratio formula:

$$\sin\theta =\frac{\text{opposite }}{\text{hypotenuse}}$

$$\sin\theta =\frac{4\sqrt{14} }{18}$

$$\csc\theta =\frac{\text{hypotenuse}}{\text{opposite }}$

$$\csc\theta =\frac{18}{4\sqrt{14} }$

$$\cos \theta=\frac{\text { adjacent side }}{\text { hypotenuse }}$

$$\cos \theta=\frac{10}{18}$

$$\sec \theta=\frac{\text { hypotenuse }}{\text { adjacent side }}$

$$\sec \theta=\frac{18 }{10}$

$$\tan \theta=\frac{\text { opposite side }}{\text { adjacent side }}$

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3 years ago

X squared+ y squared = 2 y = 2x squared – 3 Which of the following describes the system?

cluponka [151]

Answer:

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The ordered pair solutions are $(-\sqrt{\frac{7}{4}},0.5)$ , $(\sqrt{\frac{7}{4}},0.5)$ , $(-1,-1)$ , and $(1,-1)$ .

Step-by-step explanation:

I'm assuming the system is $\left \{ {x^2+y^2=2} \atop {y=2x^2-3}} \right.$ :

$x^2+y^2=2$

$x^2+(2x^2-3)^2=2$

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$x^2+4x^4-12x^2+9=2$

$4x^4-11x^2+9=2$

$4x^4-11x^2+7=0$

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$(4x^2-7)(x^2-1)=0$

$4x^2-7=0$

$4x^2=7$

$x^2=\frac{7}{4}$

$x=\pm\sqrt{\frac{7}{4}}$

$x^2-1=0$

$x^2=1$

$x=\pm1$

$y=2x^2-3$

$y=2(\pm\sqrt{\frac{7}{4}})^2-3$

$y=2({\frac{7}{4}})-3$

$y=\frac{7}{2}-3$

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$y=2x^2-3$

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2 years ago

Find the values of the pronumerals in this diagram. Write down the reason in each case.

timofeeve [1]

Answer:

see explanation

Step-by-step explanation:

a and 85 form a straight angle and are supplementary, thus

a + 85 = 180 ( subtract 85 from both sides )

a = 95

b and 85 are vertical angles and are congruent, thus

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c and 85 are corresponding angles and congruent, thus

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c and d are vertical angles and congruent, thus

d = 85

In conclusion

a = 95, b = 85, c = 85, d = 85

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