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mallardmya2006
13.10.2019 •
Mathematics
(geometry), (volume)
does anyone understand this if so could you explain them to me
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Ответ:
i dont have a clue about 16 and 17
Ответ:
∠X = 28.6° , ∠Y = 31.2° , ∠Z =120.2°
Step-by-step explanation:
Using the cosine rule, we can find one angle, then using that one anle, we can find the next angle by sine rule.
z² = x² + y² - 2(x)(y) cos (Z)
15² = 8.3² + 9² - 2(8.3)(9) cos (Z)
225 = 68.89 + 81 - 149.4 cos (Z)
Grouping the terms as,
225 - 68.89 - 81 = -149.4 cos (Z)
75.11 = -149.4 cos (Z)
cos (Z) = 75.11 / -149.4
= - 0.5
cos⁻¹ (-0.5) = 120.2°
Now we can use the sine rule as,
sin X / x = sin Z / z
To find sin X, we can rearrange the expression as,
sin X = x × sin Z / z
Plugin the values, we will get,
sin X = 8.3 × sin 120. 2 / 15
X = sin⁻¹ (0.4782) = 28.6°
As we all know that the sum of angles in a triangle is 180°.
∠X + ∠Y + ∠Z = 180°
28.6° + ∠Y + 120.2° = 180°
180° - 28.6° - 120.2° = 31.2° = ∠Y