Saved Bookmarks
| 1. |
Batao find the value of cosec 30 degree geometrically. |
| Answer» Let us take an equilateral ∆ ABC.Each angle in an equilateral triangle is 60°Therefore,\xa0{tex}\\angle A=\\angle B=\\angle C=60^{\\circ}{/tex}Let the perpendicular AD be drawn from A to side BC.Now in\xa0{tex}\\triangle {/tex}ABD and\xa0{tex}\\triangle{/tex}ACD;\xa0{tex}\\angle A D B=\\angle A D C{/tex}\xa0(as AD is perpendicular to BC)AB = AC (Since, ∆ABC is an equilateral triangle)AD = AD (Common side)Hence, by RHS criterion of congruency of triangles-{tex}\\triangle \\mathrm{ABD} \\cong \\triangle \\mathrm{ACD}{/tex}{tex}\\therefore{/tex}\xa0BD = DC (CPCT){tex}\\angle B A D=\\angle C A D=30^{\\circ}{/tex}Let the length of AB be 2a. therefore AB = BC = CD = 2aBD = half of BC = aTherefore, in ∆BADsin 30°\xa0{tex}=\\frac{B D}{A B}=\\frac{a}{2 a}=\\frac{1}{2}{/tex}\xa0{tex}\\therefore {/tex}\xa0Cosec 30° = 2 | |