Question

in the given figure angle B =60°,AB=16 cm and BC =23 cm calculate 1.BE 2. AC​

Answer 1

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Answer 2

Given:

Angle B=60°, AB=16cm, and BC=23cm

To find:

The length of BE and AC

Solution:

The length of BE=8cm and AC=20.42cm

We can find the length by following the steps given below-

We know that the length of BE and AC can be calculated using the properties of right-angled triangles.

In ∆AEB, angle B=60° and angle AEB=90°.

Using trigonometry, we can find the length of AE.

Sin60°= AE/AB

√3/2=AE/16

AE=16×√3/2

AE=8√3 cm

Similarly, Cos60°=BE/AB

1/2=BE/16

BE=8cm

Also, BC=BE+EC

23=8+EC

EC=23-8

EC=15cm

In ∆AEC, on using the Pythagoras theorem, we get

AE²+EC²=AC²

Putting the values,

8√3²+15²= AC²

192+225=AC²

417=AC²

AC=20.42cm

Therefore, the length of BE=8cm and AC=20.42cm.