diff --git a/Grade 10/Math/MPM2DZ/Trig Quiz 1.md b/Grade 10/Math/MPM2DZ/Trig Quiz 1.md index 1aba40e..6a4b93f 100644 --- a/Grade 10/Math/MPM2DZ/Trig Quiz 1.md +++ b/Grade 10/Math/MPM2DZ/Trig Quiz 1.md @@ -44,4 +44,52 @@ x = 17.1428571 \approx 17.14 y = 26.25 -``` \ No newline at end of file +``` + +# Question 2 + +```math + +h = b \sin A \\ + +h = 11.3 \sin 32 \\ + +h = 5.99 \\ + +\because h \le 6.8 \le 11.3 \\ + +\therefore 2 \triangle 's \text{ exist} \\ + +\text{ Lets call point } T \text{ is the height that is perpendicular on side } AB \text{ and connects to point } C. \text { and } B^\prime \text{ be the other possible point of } B. +``` +------------------------- +$`\text{ Case } 1:`$ + +$`\angle CB^\prime T = \sin^{-1} \Bigl(\dfrac{5.99}{6.8} \Bigr)`$ + +$`\angle CB^\prime T = 61.75^o`$ + +$`\angle AB^\prime C = 180 - 61.75 = 118.25^o (\text{ Complentary Angle Theorem})`$ + +$`\angle ACB^\prime = 180 - 61.75 - 32 = 86.25^o (\text{ASTT})`$ + +$`\dfrac{AB}{\sin \angle ACB^\prime} = \dfrac{CB^\prime}{\sin A}`$ + +$`\dfrac{AB}{\sin86.25} = \dfrac{6.8}{\sin 32}`$ + +$`AB = \dfrac{\sin 86.25 \times 6.8}{\sin32}`$ + +$`AB = 12.8`$ + +------------------------- +$`\text{ Case} 2: `$ + +$`\angle ABC = 61.75`$ + +$`\angle ACB = 180 - 32 - 61.75 = 86.25^o (\text{ ASTT})`$ + +$`\dfrac{AB}{\sin C} = \dfrac{CB}{\sin A}`$ + +$`\dfrac{AB}{\sin 86.25} = \dfrac{6.8}{\sin 32}`$ + +$`AB = \ No newline at end of file