Question

ABC right angled at B AB = 5cm and ACB = 30 Determine the lengths of the side BC and AC

Answer 1

we know that sin∅=opp/hyp

sin30=AB/AC

1/2=5/AC

by cross multiplying, AC=10

similarly,  cos∅=adj/hyp

cos30=BC/AC

√3/2=BC/10

by cross multiplying, 2BC=10√3

BC=5√3

Answer 2

Answer:-

$\large\sf{\frac{AB}{BC}=tanC}$

$\large\sf{i.e.,\:\frac{5}{BC}=tan30°=\frac{1}{√3}}$

$\large\sf{which\:gives\:5√3cm}$

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$\small\sf{to\:find\:the\:length\:of\:the\:side\:AC,}$

$\large\sf{we\:consider,}$

$\longrightarrow$$\large\sf{sin30°=\frac{AB}{AC}}$

$\longrightarrow$$\large\sf{\frac{1}{2}=\frac{5}{AC}}$

$\longrightarrow$$\large\sf{AC=10cm}$

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$\large\sf{By\:using\:Pythagoras\:theorem,}$

$\longrightarrow$$\large\sf{AC=√{AB}^{2}+{BC}^{2}}$

$\longrightarrow$$\large\sf{√{5}^{2}+{(5√3)}^{2}}$

$\longrightarrow$$\large\sf{10cm}$