Question

А
12. In the given figure,
B = 60°, AB = 16 cm
and BC = 23 cm.
Calculate
(1) ВЕ (ii) AC​

Answer 1

Answer:

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