In an isosceles triangle, its two equal sides are 20cm each, and the angle between them is 30degrees. What is the area of the triangle for c

Question

In an isosceles triangle, its two equal sides are 20cm each, and the angle between them is 30degrees. What is the area of the triangle for class IX?

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2 months 2021-11-28T12:56:50+00:00 1 Answer 0 views 0

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    2021-11-28T12:58:01+00:00

    Answer:

    The constraint here is – NOT to use Trigonometry.

    I have tried not to use any trigonometric property or angle formulas.

    The method goes as follows –

    Triangle is Isosceles, means it 2 sides are equal.

    Now, if its 2 sides are equal, we have to think of 2 line segments of equal lengths.

    Question arises, where we can find it…!!

    A simple solution to question is, Radii of a Circle .

    2 radius of the same circle, are always equal.

    So, lets assume a circle with 2 radii.

    These radii, touch each other at O, at 30°. ——————-(1)

    Let these 2 radii be 2 sides of the given triangle. (Length = 20 Cm)

    (Given that these 2 sides make 30° angle between them). ——— (2)

    Now we have a circle. Inside it we have a triangle which 2 sides are the 2 different radii of the circle making an angle 30°.

    Suppose we have a triangle which has 90° angle making between its 2 radii. Here also side = 20 Cms.

    Area of this triangle (Making 90°) will be = (1/2)*20*20 = 200 cm*cm. ——(3)

    Now we are talking about a circle where the area is always a function of angle. Area of Circle = π*r*r

    And Area of Segment of Circle = π*r*r*Θ/360 ——————-(4)

    Here except Θ, everything is constant, for a given circle.

    Area α Θ (Proportional). ———————— (5)

    But here we need Area of triangle, which is not Area of Segment.

    Since, the triangle is a part of the segment itself.

    We can write, Area of Triangle α Θ (Proportional). ————(6)

    Using the above direct proportionality, from Eqn(6).

    From Eqn(3), we know,

    For 90°, we have 200.

    For 30°, we will get 200/3 cm*cm

    So, Answer 200/3 cm*cm

    Step-by-step explanation:

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