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GuDViN [60]
2 years ago
13

Find x, find jl . any help is deeply appreciated :) !​

Mathematics
1 answer:
Doss [256]2 years ago
4 0

Answer:

6. x = 15

7. JL = 78

Step-by-step explanation:

6. 8x - 23 = ½(10x + 44) (midsegment theorem)

Multiply both sides by 2

2(8x - 23) = 10x + 44

16x - 46 = 10x + 44

Collect like terms

16x - 10x = 46 + 44

6x = 90

Divide both sides by 6

x = 90/6

x = 15

7. MN = 5x - 16

JL = 4x + 34

MN = ½(JL) (midsegment theorem)

5x - 16 = ½(4x + 34) (substitution)

2(5x - 16) = 4x + 34

10x - 32 = 4x + 34

Collect like terms

10x - 4x = 32 + 34

6x = 66

x = 66/6

x = 11

JL = 4x + 34

Plug in the value of x

JL = 4(11) + 34 = 44 + 34

JL = 78

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Veseljchak [2.6K]

cos θ = \frac{-4\sqrt{65} }{65}, sin θ = \frac{-7\sqrt{65} }{65}, cot  θ  = 4/7, sec  θ = \frac{-\sqrt{65} }{4}, cosec  θ  = \frac{-\sqrt{65} }{7}

<h3>What are trigonometric ratios?</h3>

Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin θ: Opposite Side to θ/Hypotenuse

Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos

Cos θ: Adjacent Side to θ/Hypotenuse

Sec θ: Hypotenuse/Adjacent Side & 1/cos θ

Analysis:

tan θ = opposite/adjacent = 7/4

opposite = 7, adjacent = 4.

we now look for the hypotenuse of the right angled triangle

hypotenuse = \sqrt{7^{2} + 4^{2} } = \sqrt{49+16} = \sqrt{65}

sin θ = opposite/ hyp = \frac{7}{\sqrt{65} }

Rationalize, \frac{7}{\sqrt{65} } x \frac{\sqrt{65} }{\sqrt{65} } = \frac{7\sqrt{65} }{65}

But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.

Therefore, sin θ = - \frac{7\sqrt{65} }{65}

cos   θ  = adj/hyp = \frac{4}{\sqrt{65} }

By rationalizing and knowing that cos  θ  is negative, cos θ  = -\frac{-4\sqrt{65} }{65}

cot θ  = 1/tan θ  = 1/7/4 = 4/7

sec θ  = 1/cos θ  = 1/\frac{4}{\sqrt{65} } = -\frac{-\sqrt{65} }{4}

cosec θ  = 1/sin θ  = 1/\frac{\sqrt{65} }{7} = \frac{-\sqrt{65} }{7}

Learn more about trigonometric ratios: brainly.com/question/24349828

#SPJ1

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