From d2278cc4c884af13db39733ce585fdf4437c5624 Mon Sep 17 00:00:00 2001 From: Alexander Molnar <37451552+BTmathic@users.noreply.github.com> Date: Thu, 21 Mar 2019 06:15:38 -0400 Subject: [PATCH] Fixed formatting (#34461) Fixed multi-line expressions to display properly --- .../english/mathematics/law-of-sines/index.md | 51 +++++++++---------- 1 file changed, 23 insertions(+), 28 deletions(-) diff --git a/guide/english/mathematics/law-of-sines/index.md b/guide/english/mathematics/law-of-sines/index.md index 548870e6aa..bb28057123 100644 --- a/guide/english/mathematics/law-of-sines/index.md +++ b/guide/english/mathematics/law-of-sines/index.md @@ -1,16 +1,16 @@ --- title: Law of Sines --- -## Law of Sines +## Law of sines -The Law of Sines simply states that: - -Sin(A) Sin(B) ------- = ------ - a b - -Where "A" and "B" are angle measures, and "a" and "b" are their corresponding side lengths -This law is used with triangles, when two angles and one side length are known, here is an example: +The law of sines states that +``` +sin(A) sin(B) sin(C) +------ = ------ = ------ + a b c +``` +where A, B and C are angles, and a, b and c are their corresponding (opposite) side lengths. This law is used with triangles, when two angles and one side length are known. For example, consider the triangle +``` b ____________ \ 75/ @@ -19,26 +19,21 @@ ____________ \ / \30/ \/ - -In this problem, everything is defined except for "b," therefore, we can use the law of sines to find it. For this problem, I will -refer to the corresponding angle and side as "A" and "a": - -Sin(A) Sin(B) Sin(75) Sin(30) ------- = ------ ===> ------- = ------- +``` +In this (isoceles) triangle, we know everything except for b, the angle opposite B = 30°, therefore, we can use the law of sines to find it. With A = 75 and a = 6, we have +``` +sin(A) sin(B) sin(75) sin(30) +------ = ------ ===> ------- = ------- a b 6 b - -For evaluating the Sines, I used a calculator. I can cross multiply the two sides of the equation, which evaluates as: - - 6 * Sin(30) +``` +Cross multiplying gives +``` + 6 * sin(30) b = ----------- sin(75) +``` +which simplifies to, approximately, -Which comes out to - -b = 3.106 - - -#### More Information: - - - +
+ b ≈ 3.106 +