Question

in a triangle abc d is a point on side ab and e is a point on side ac such that angle ade = angle abc, ad=2cm, bd=3cm, ae=3 cm find ce plss as soon as possible​

Answer 1

Solution :-

Let CE is equal to x cm .

In ∆ADE and ∆ABC we have,

→ ∠ADE = ∠ABC { given }

→ ∠DAE = ∠BAC { common }

So,

→ ∆ADE ~ ∆ABC { By AA similarity }

then,

→ AD/AB = AE/AC { when two ∆'s are similar, corresponding sides are in same ratio . }

→ 2/(2 + 3) = 3/(3 + x)

→ 2/5 = 3/(3 + x)

→ 2(3 + x) = 3 * 5

→ 6 + 2x = 15

→ 2x = 15 - 6

→ 2x = 9

→ x = 4.5 cm (Ans.)

Hence, length of CE is equal to 4.5 cm .

Answer 2

To find CE in triangle ABC, we can use the Law of Sines and the given lengths of AD, BD, and AE. By finding the angles CAB and ACE, we can calculate the length of CE using trigonometry.

Step-by-step explanation:

In triangle ABC, point D is on side AB and point E is on side AC. Given that angle ADE is equal to angle ABC, AD = 2 cm, BD = 3 cm, and AE = 3 cm, we need to find the length of CE.

First, we can use the Law of Sines to find angle CAB: sin(CAB) = (BC/AB) = (3/5). Therefore, angle CAB is approximately 36.87 degrees.

Since angle ADE is equal to angle ABC, we can use the Law of Sines again to find CE: sin(CEA) = (AE/AC) = (3/CE). Rearranging the equation, we get CE = (3/sin(CEA)). To find sin(CEA), we can use the sine of the angle opposite to it in triangle ACE. The equation becomes CE = (3/sin(180 - CAB - CEA)).

Using the angles CAB and ACE, we have CEA = (180 - 36.87 - ACE). Plugging in the values, we get CE = (3/sin(180 - 36.87 - ACE)).

Learn more about Triangle Geometry