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3 years ago

Find QN. Please show all the work on how you got your answer

Mathematics

1 answer:

Effectus [21]3 years ago

3 0

QN = 28

Solution:

Given MNPQ is a parallelogram.

QT = 4x + 6 and TN = 5x + 4

To find the length of QN:

Let us solve it using the property of parallelogram.

Property of Parallelogram:

Diagonals of the parallelogram bisect each other.

Therefore, QT = TN

⇒ 4x + 6 = 5x + 4

Arrange like terms together.

⇒ 6 – 4 = 5x – 4x

⇒ 2 = x

⇒ x = 2

Substitute x = 2 in QT and TN

QT = 4(2) + 6 = 14

TN = 5(2) + 4 = 14

QN = QT + TN

= 14 + 14

QN = 28

The length of QN is 28.

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

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

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

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we can find the third side using the Pythagoras theorem.

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

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

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

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

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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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