# Two altitudes of an isosceles triangle are equal to 20 cm and 30 cm. determine the possible measures of the base angles of the triangle

1
by math9

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by math9

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let say..an isoseles triangle ABC where C in vertical that is perpendiular to point E ( base mid of AB) , WHOSE ALTItude is 30cm, at angle B has a slant line whose distance is 20 perpndicular to point D (mid of Slope /line AC) angle ABD.(small triangle)

i pressume angle A would be the base angle of the triangle.

here are the ratio and proportion;

30/AE =20/AD;

AD/AE =20/30 =2/3

AD=2AE/3...................1.

of course we believe this Phytagorean theorem;

angle ABD;

[AB]^2=20^2 + [AD]^2..........2.

tan A =30/EB (angle ABD) =30/AE (angle AED);

hence: 30/EB= 30/AE;

AE/EB=1;

AE=EB ..(as a proof , u can see that if you draw the triangle)

also we have this arrangement of triangle ABC..

AB= AE +EB;

AB=2AE................3.

@2 &1

[2AE]^2=400 +[ 4AE^2]/9;

4AE^2=400 +[4AE^2]/9;

36AE^2=3,600 +4AE^2;

32AE^2=3,600;

AE=10.6CM...

tan A= 30/10.6

A=71 degrees;;

the smaller angle of ABD is

90-71 = 19 degrees...

Just take a review , so much the better if i can post my figure for you analize more , algebraically...ty 9 i dont have a sci cal..)