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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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