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3 years ago

Please solve this problem

Mathematics

1 answer:

asambeis [7]3 years ago

8 0

Answer:

(4) 0

Step-by-step explanation:

Given:

cos²27°×cos²34°×...×cos²167 = ?

Looking at the angles measures, they form series of:

27, 34, 41, ..., 167

This is AP with the first term of 27 and common difference of 7

We can see one of the terms of this AP is 90

27+9*7 = 27 + 63 = 90

Since cos 90° = 0 ⇒ cos²90° = 0 and therefore given series equals to zero as one of the terms of multiplication is zero.

So correct answer choice is Option 4) 0

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Answer:

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Step-by-step explanation:

a) Since $AB \perp BC$ , the length of segment $AC$ is determined by Pythagorean Theorem, that is:

$AC = \sqrt{(5\,cm)^{2}+(3\,cm)^{2}}$

$AC \approx 5.831\,cm$

The length of segment AC is approximately 5.831 centimeters.

b) Since $AB \perp BC \perp AD$ , the length of segment $AD$ is determined by this Pythagorean identity:

$AD = \sqrt{(3\,cm)^{2}+(5\,cm)^{2}+(4\,cm)^{2}}$

$AD \approx 7.071\,cm$

The angle ACD is determined by the following trigonometric expression:

$\cos C = \frac{AC}{CD}$

$\cos C = \frac{5.831\,cm}{7.071\,cm}$

$\cos C = 0.825$

$C = \cos^{-1} 0.825$

$C \approx 34.448^{\circ}$

The angle ACD is approximately 34.448º.

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I believe the answer is A. 20, 30, 40 is NOT a pythagorean triple.

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3 years ago

(09.02)

dmitriy555 [2]

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