12. In the given figure,
angleB = 60°, AB = 16 cm
and BC = 23 cm.
Calculate :
(i) BE (ii) AC.
Answers
sorry please send the bigger I don't able to understand where is we I think it is in the centre of the A and C if it then you make it and we have to length that we e60 and if it's pass from its Centre then V is 30 and b is 16 we don't have the value of that so I am not able to answer you please send the figure then I promise you that I will answer your question I know that I think I read this question in my 7th class are you in 7th class I read it and is sorry but I forgot my question so you have please send me pic and I am able to answer you is Mark please as brain list
If angle B = 60°, AB = 16 cm and BC = 23 cm, then BE = 8 cm and AC = 20.42 cm.
Step-by-step explanation:
∠B = 60°
AB = 16 cm
BC = 23 cm
Case (I): Measure of side BE
Referring to the figure attached below,
Consider ∆ ABE, applying the trigonometry ratio of triangles, we get
cos θ = base/hypotenuse = BE/AB
⇒ cos 60° = BE/16
⇒ ½ * 16 = BE
⇒ BE = 8 cm ….. (i)
Also, in ∆ ABE,
tan θ = perpendicular/base = AE/BE
⇒ tan 60° = AE/8 ….. [from (i)]
⇒ AE = 8√3 cm ….. (ii)
Case (II): Measure of side AC
From the figure, we get
EC = BC – BE = 23 – 8 = 15 cm
Now, consider ∆ AEC, applying the Pythagoras theorem, we get
AC² = AE² + EC²
⇒ AC = √[(8√3)² + 15²]
⇒ AC = √[192 + 225]
⇒ AC = √[417]
⇒ AC = 20.42 cm
Thus, BE = 8 cm and AC = 20.42 cm .
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