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Aleonysh [2.5K]
3 years ago
14

I really need help with number nine

Mathematics
2 answers:
Trava [24]3 years ago
7 0
The answer would be:
C) 190
snow_lady [41]3 years ago
3 0
Take a more clear picture then I will help you
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Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β
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Answer:

From given relation the value of β is 37.5°

Step-by-step explanation:

Given as :

α and β are two acute angles of right triangle

Acute angle have measure less than 90°

Now given as :

sin(\frac{x}{2} + 2x) = cos(2x +\frac{3x}{2})

Or, cos(90° - (\frac{x}{2}+2x)) =  cos(2x +\frac{3x}{2})

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Or, 90° =  2x+\frac{3x}{2} + \frac{x}{2}+2x

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So, x =  \frac{90}{6} = 15°

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So, sin(\frac{x}{2} + 2x) = sin\frac{75}{2}

∴  The value of Ф_1 = \frac{75}{2} = 37.5°

Similarly  cos(2x +\frac{3x}{2}) =  cos(30 +\frac{45}{2})

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∵ β   α

So, As 37.5°52.5°

∴ β = 37.5°

Hence From given relation the value of β is 37.5°  Answer

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