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Question-67860




Question Number 67860 by TawaTawa last updated on 01/Sep/19
Commented by TawaTawa last updated on 01/Sep/19
Find angle  a
$$\mathrm{Find}\:\mathrm{angle}\:\:\mathrm{a} \\ $$
Commented by mr W last updated on 01/Sep/19
a=72°
$${a}=\mathrm{72}° \\ $$
Commented by TawaTawa last updated on 01/Sep/19
Correct, please workings sir
$$\mathrm{Correct},\:\mathrm{please}\:\mathrm{workings}\:\mathrm{sir} \\ $$
Answered by mr W last updated on 01/Sep/19
let BC=1  ∠B=12+36=48=30+18=∠C  ⇒AB=AC=((BC)/2)×(1/(cos ∠B))=(1/(2 cos 48°))  ((BD)/(sin 30°))=((BC)/(sin (12+30)))=(1/(sin 42°))=(1/(cos 48°))  ⇒BD=(1/(2 cos 48°))=BA  2a+36=180  ⇒a=((180−36)/2)=72°
$${let}\:{BC}=\mathrm{1} \\ $$$$\angle{B}=\mathrm{12}+\mathrm{36}=\mathrm{48}=\mathrm{30}+\mathrm{18}=\angle{C} \\ $$$$\Rightarrow{AB}={AC}=\frac{{BC}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{cos}\:\angle{B}}=\frac{\mathrm{1}}{\mathrm{2}\:\mathrm{cos}\:\mathrm{48}°} \\ $$$$\frac{{BD}}{\mathrm{sin}\:\mathrm{30}°}=\frac{{BC}}{\mathrm{sin}\:\left(\mathrm{12}+\mathrm{30}\right)}=\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{42}°}=\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{48}°} \\ $$$$\Rightarrow{BD}=\frac{\mathrm{1}}{\mathrm{2}\:\mathrm{cos}\:\mathrm{48}°}={BA} \\ $$$$\mathrm{2}{a}+\mathrm{36}=\mathrm{180} \\ $$$$\Rightarrow{a}=\frac{\mathrm{180}−\mathrm{36}}{\mathrm{2}}=\mathrm{72}° \\ $$
Commented by TawaTawa last updated on 01/Sep/19
God bless you sir
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Commented by TawaTawa last updated on 02/Sep/19
Sir, why did you let  BC = 1,  and when can i use it in question.
$$\mathrm{Sir},\:\mathrm{why}\:\mathrm{did}\:\mathrm{you}\:\mathrm{let}\:\:\mathrm{BC}\:=\:\mathrm{1},\:\:\mathrm{and}\:\mathrm{when}\:\mathrm{can}\:\mathrm{i}\:\mathrm{use}\:\mathrm{it}\:\mathrm{in}\:\mathrm{question}. \\ $$
Commented by mr W last updated on 03/Sep/19
you can also  let BC=a if you like. if  you are only interested at angles, the  absolute values of the lengthes are not  important, only the ratio between them.
$${you}\:{can}\:{also}\:\:{let}\:{BC}={a}\:{if}\:{you}\:{like}.\:{if} \\ $$$${you}\:{are}\:{only}\:{interested}\:{at}\:{angles},\:{the} \\ $$$${absolute}\:{values}\:{of}\:{the}\:{lengthes}\:{are}\:{not} \\ $$$${important},\:{only}\:{the}\:{ratio}\:{between}\:{them}. \\ $$
Commented by TawaTawa last updated on 06/Sep/19
God bless you sir
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

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