Question

In a triangle ABC. AB=6√3 perpendicular is drawn from point A on BC at E of length 9 and EC=3√3. Find angle A

Answer 1

Answer:

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∠A = 60ﾟ

Step-by-step explanation:

Given :-

AB=6√3

perpendicular from point A on BC at E of length 9

EC=3√3

To find :-

Find angle A

Proof :-

In △AEB,

AE = 9

AB = 6√3. [GIVEN ]

Let's Find BE,

Since we know that AE is perpendicular.

So , by pythagorus theorem,

(AB)² = (AE)² + (EB)²

(6√3)² = (9)² + (EB)²

(36 × 3) = 81 + (EB)²

108 = 81 + (EB)²

108 - 81 = (EB)²

27 = (EB)²

√27 = EB

3√3 = EB

BC = BE + CE

BC = 3√3 + 3√3

BC = 6√3

Similarly let's find AC,

In △AEC,

Since we know that AE is perpendicular.

Since we know that AE is perpendicular.So , by pythagorus theorem,

(AC)² = (AE)² + (EC)²

(AC)² = (9)² + (3√3)²

(AC)² = 81 + 27

(AC)² = 108

(AC)² = 6√3

Now,

In △ABC,

AB = AC = BC = 6√3

SINCE,

All sides of the △ABC are equal,

therefore,

it is an equilateral triangle.

and we know that all angles of an equilateral triangle are 60ﾟ.

hence,

∠A = 60ﾟ