Question

Ratio of three angles of a triangle is 1:2:3. Find the area.​

Answer 1

Answer:

7290000 sq. units

Step-by-step explanation:

GIVEN:

The ratio of three angles of a triangle = 1 : 2 : 3

TO FIND:

The Area of the Triangle

SOLUTION:

Let, the angles of the triangle be x, 2x, and 3x

We know that,

• The sum of all angles of a triangle = 180°

therefore,

=> x + 2x + 3x = 180

=> 6x = 180

=> x = 30

Now, the angles are :-

• x = 30°
• 2x = 60°
• 3x = 90°

Since, one of the angles is 90°, it is a right-angled triangle.

The formula for the area of a right angled triangle when only angles are given :-

• area = (bc × ba)/ 2

[NOTE: For seeing the angles b, c and a take help from the attachment, here i am taking c = 60 and a = 30]

=> Area = (90 × 60 × 90 × 30)/ 2

= 90 × 90 × 30 × 30

= 8100 × 900

= 7,290,000 sq. units

hence, the area of the given triangle is 7290000 sq. units

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[[ EDIT: I am not sure about the formula ive used here, sorry :/  I just found this formula somewhere, one side must be known to find the area using the formula.

If we Assume that the shorter leg of a 30 60 90 triangle is equal to a. Then:

• the second leg is equal to a√3

• the hypotenuse is 2a

• the area is equal to a²√3/2

Legs of a triangle are the sides of the triangle ]]

                             

Hope this helps!