Respuesta :

Answer:

x= 90 degree

y= 43 degree

Step-by-step explanation:

We have been given an isosceles triangle being two sides equal AB and AC

By the property of isosceles triangle

The sides which are equal will have same base angle

Hence, ∠ABC=∠ACB=

We know that sum of angles of triangle is  

∠ABC+ ∠ACB+∠BAC=      (1)

Since, ∠BAC is the bisector so, ∠BAD and ∠DAC are equal which is  

Now, substituting the values in (1) we get:

Now, we will consider ΔABD to find x

,∠ADB=∠ABD=

Now, Apply the sum of angles of triangle is  we get:

clarch19

Answer:

x = 8[tex]\sqrt{7}[/tex]

y = 4[tex]\sqrt{21}[/tex]

Step-by-step explanation:

use the altitude rule to find the height of the triangle first

12/h = h/16

h² = 12x16

h = [tex]\sqrt{192}[/tex]

h = [tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{3}[/tex] = 8[tex]\sqrt{3}[/tex]

now you can use the Pythagorean Theorem with height of 8[tex]\sqrt{3}[/tex] along with the other leg of 12 to find 'y'; which comes out to be [tex]\sqrt{336}[/tex] or [tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{21}[/tex]

then use the Pythagorean Theorem with height of 8[tex]\sqrt{3}[/tex] along with the other leg of 16 to find 'x'; which comes out to be [tex]\sqrt{448}[/tex] or [tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{7}[/tex]

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