On a coordinate plane, Point C is at (-3,5) and Point D is at (4,9). What is the distance from point C to point D?

Mathematics

1 answer:

VladimirAG [237]2 years ago

8 0

Answer:

5 $\sqrt[\\]{3} \\$ or about 8.66

Step-by-step explanation:

To find the distance of any line, you have to use distance formula.

$\sqrt{(y-y_{1} )^{2} + (x-x_{1} )^{2}$

So, we insert our points:

$\sqrt{(5-9 )^{2} + (-3-4 )^{2}$

Then you solve, and should end up with $\sqrt{75}$ . Either you can simplify it for an exact number, or you can round. It depends on what the directions ask for.

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Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$