When will I need to reject the angle ?
2015-08-29 5:08 pm
When using the sine formula, sometimes when I calculated the angle, usually the answer would show you that there should be another answer, either acceptable or being rejected. I think I am not quite clear about the situations when I need to reject or keep the answer (even after reading textbooks) . So may Math experts follow up this and the following question? thanks a lot!
回答 (2)
2015-08-30 7:03 am
✔ 最佳答案
When using sine formula to solve a triangle (said, to find angle A), you will find "sinA = 0.xxx" and then you will A = α.The sine function is positive in both the 1st and 2nd quadrants. Therefore, both "A = α" and "A = 180° ‒ α" fulfill that "sinA = 0.xxx".
"A = 180° ‒ α" should be rejected if
- the sum of interior angles of the triangle exceeds 180°
- A is NOT the greatest interior angle.
Otherwise, accept "A = 180° ‒ α".
====
1.
15 / sinθ = 11 / sin35° (sine formula)
sinθ = sin35° × (15/11)
sinθ = 0.7821
θ = 51.46° or θ = 180° ‒ 51.46°
θ = 51.46° or θ = 128.54°
(Because 128.54° + 35° < 180° and there is NO information to show that B is NOT the greatest angle of the triangle, accept "θ = 128.54°".)
2015-08-29 5:29 pm
大概看不知領悟有錯嗎?
角都有對邊,求另一角或邊,一般用正弦定理.
有三邊長和任一角,一般用餘弦定理.
15/sin西塔=11/sin35度
==>sin西塔=0.78214 (近似值)
==>西塔=51.46度 (近似值) 或另一解為180-51.46=128.54(度) 因沒說是銳角且sin西塔在一,二象限都是正,所以鈍角也可以.
角都有對邊,求另一角或邊,一般用正弦定理.
有三邊長和任一角,一般用餘弦定理.
15/sin西塔=11/sin35度
==>sin西塔=0.78214 (近似值)
==>西塔=51.46度 (近似值) 或另一解為180-51.46=128.54(度) 因沒說是銳角且sin西塔在一,二象限都是正,所以鈍角也可以.
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