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3 years ago

△ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches.

1 answer:

7 0

<span>△ABC∼△DEF
</span>Height of <span>△ABC: h1=20 inches
</span>Height of △DEF: h2=24 inches
<span>Ratio of the area of △ABC to the area of △DEF: R=?
</span>
R=(h1/h2)^2
R=[ (20 inches) /(24 inches) ]^2
R=(5/6)^2
R=5^2/6^2
R=25/36

Answer: T<span>he ratio of the area of △ABC to the area of △DEF is 25/36</span>

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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 = $\frac{-\sqrt{65} }{7}$

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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

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tan θ = opposite/adjacent = 7/4

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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 = - $\frac{7\sqrt{65} }{65}$

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

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

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

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