Question

in ΔABC, AB=(X-3)Cm, BC=(X+3)Cm, AC=8Cm AND ∠BAC=60°
USE COSINE RULE TO FIND THE VALUE OF X.

Answer 1

The half angle formula for sine is simple:

Let the sides opposite to the angles A,B,C of a non-spherical triangle ( A+B+C=π ) be denoted by the corresponding small letters a,b,c respectively. Also let s be the semi-perimeter of the triangle. Then,

$\sin( \frac{A}{2} ) = \sqrt{ \frac{(s - b)(s - c)}{bc} }$

$\bold{where \: s, \: \frac{a + b + c}{2} }$

Here A=60∘, b=8, c=x−3

$\bold {Also \: s, = \frac{2x + 8}{2} = x + 4}$

Using the formula,

$\implies \: \sin \: 30 = \sqrt{ \frac{(x - 4)(x + 4 - x + 3)}{8(x - 3)} }$

$\implies \: \frac{1}{2} = \sqrt{ \frac{7(x - 4)}{8(x - 3)} }$

Squaring and cross multiplying,

$⟹2(x−3)=7(x−4)$

$⟹ \frac{22}{5}$

$</p><p>⟹x=4.4 \: cm</p><p></p><p></p><p>$

Answer 2

Step-by-step explanation:

Characteristics of cork are as follow

Cells of cork are dead, compactly arranged and have no intercellular spaces. It forms bark of the tree, which is several layers thick. ... Cork is formed by secondary Lateral Meristem called cork cambium. The mature cork becomes dead and filled with tannin, resin.