Question

В равнобедренном треугольнике АВС к основанию АС проведена высота BD . Чему равен угол ВАС ,если <DBC=20(градусам )? Ответ дайте в градусах

Answer 1

В равнобедренном треугольнике высота является биссектрисой, след-но угол DBA= углу DBC=20 гр. Треугольник DBA прямоугольный. Угол ВАС=180-90-20=70 градусов. 

Answer 2

DBC=ABD следовательно ABD=20
B=DBC+ABD = 20+20=40
Тре-ник ABC - равнобедренный следовательно A=C. Сумма углов треу-ника равна 180. A=(180-40):2= 70 . A= 70 градусов

Answer 3

Finding the Angle BAS in an Isosceles Triangle

To find the measure of angle BAS in an isosceles triangle ABC, where BD is the altitude drawn to the base AC and angle DBC is given as 20 degrees, we can use the properties of isosceles triangles.

In an isosceles triangle, the base angles (angles opposite the equal sides) are congruent. Therefore, angle ABC is equal to angle ACB.

Let's denote angle ABC (or ACB) as x.

Since angle DBC is given as 20 degrees, we can write the following equation:

x + 20 + x = 180

Simplifying the equation, we have:

2x + 20 = 180

Subtracting 20 from both sides:

2x = 160

Dividing both sides by 2:

x = 80

Therefore, angle ABC (or ACB) is equal to 80 degrees.

Since angle BAS is an exterior angle to triangle ABC, it is equal to the sum of the two remote interior angles, which are angle ABC and angle ACB.

So, angle BAS = angle ABC + angle ACB = 80 + 80 = 160 degrees.

Hence, the measure of angle BAS in the given isosceles triangle ABC, with angle DBC as 20 degrees, is 160 degrees.

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