Understanding the Law of Sines and Cosines (Math Problem Sample)
the mathematics problem required knowledge on the law of sines and cosines. to solve the problem i first drew a triangle for clear demonstration of the question at hand. t
the triangle was labelled abc. the measurements given in the question were then filled in the triangle.
THEN THE LAW OF SINES AND COSINES IS DEFINED.
then we used the law of sines and cosines to find angle a, as required by the question.
Question 1Solve for α in the oblique triangle ABC; AB = 30; AC = 15 and angle B = 20°
Oblique triangle ABC; AB = 30; AC = 15 and angle B = 20°
1 Type out the two equations substituting the numbers from the diagram.DemonstrationDrawing out the triangle first:
10096502971800A
c= 30 b=15 B a Cangle ABC=20° (β)angle ACB=Ɣangle BAC=α ( This is the angle in question) Solution
Equation 1 (obtained from the law of cosines)
b2=a2+c2-2ac(cos b)(We are going to choose this equation because we only have one unknown. That is, a.) Substituting the values from the diagram above, where: b = 15 c =30
β = 20°)Therefore Equation 1 is;
152=a2+302-2a.30.(cos20°)
Other Topics:
- Examples of Logical ProblemsDescription: 1 ∀x(Ax → Bx) 2 ∀x (Ax→Cx) 3 Ad→Bd 1, ∀Elim 4 Ad→Cd 2, ∀Elim 5 Ad Assumption for CP 6 Bd 3,5 →Elim 7 Cd 3,4 → Elim 8 Bd & Cd 6,7 & Intro 9 Ad → (Bd &Cd) 5,-8 →Intro 10 ∀x[Ax→(Bx&Cx)] 9, ∀Intro 1 ∀x(¬Cx →¬Ax) 2 ∃xCx → (∃x¬(¬Bx V ¬ Dx) 3 ¬(¬∃xAx V ∃xBx) Assumption for IP 4 ¬Cd → ¬Ad 1, ∀ Elim 5 ...6 pages/≈1650 words| No Sources | Other | Mathematics & Economics | Math Problem |
- Solving Mathematical Equation Involving IntegrationDescription: To evaluate ʃ x sin 3x dx, we use the method of integration by parts given by the formula; ʃ u dv = uv-ʃ v du Let u = x, dv = sin 3x; then, v= -cos 3x and du = dx. Now substituting in the formula we get; ʃ x sin 3x dx = x-1/3cos 3x-ʃ-1/3cos 3x dx = -1/3cos 3x+1/9sin 3x+C, where C is a constant. ...2 pages/≈550 words| No Sources | Other | Mathematics & Economics | Math Problem |
- Mathematics exam setting. Mathematics & Economics Math ProblemDescription: 5x x 52y = 25 and 32x x 3y = QUOTE (3 Marks) Solve for x in (log x)2 = QUOTE (3 marks) Solve for x in the equation. (3 marks) 9(22x+ 2) – 41(2x) + 8 = 0 Solve for x in the equation. EMBED Equation.3 (3 marks) Solve for x in the given equation. (3 marks) 64x – 121 = 7...1 page/≈550 words| 1 Source | Other | Mathematics & Economics | Math Problem |
