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1 year ago

Pleeeaaasseeee help (questions in photo) will mark brainliest

Mathematics

1 answer:

KIM [24]1 year ago

5 0

Answer:

a. 0.8727rad

b. 5.585rad

that should be correct, if not, i apologize T_T

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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 $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

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

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

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

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3 years ago

When constructing an inscribed circle, which point is the center of the circle?

lesantik [10]

Answer:

D. The intersection of the angle bisectors.

Step-by-step explanation:

The incenter is equidistant from each of the sides of the triangle. An angle bisector is the set of points equidistant from the sides, so the incenter is the place where the angle bisectors meet.

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3 years ago

Which number line below correctly represents the expression -3 + 4?

Archy [21]

Answer:

1st answer

Step-by-step explanation:

First you subrtract 3 from 0 then add 4 to -3

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3 years ago

If the area of the blue square is 25 in2 and the area of the green square is 15 points

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Answer:

144 in²

Step-by-step explanation:

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2 years ago

Can someone please help me?

Radda [10]

Answer:

44 degrees

Step-by-step explanation:

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2 years ago

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