# From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = 52 , then what is the height of ∆ABC? - Geometry

Sum

From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = 5sqrt(2) , then what is the height of ∆ABC?

#### Solution

AB = BC     ......[Given]

∴ ∠A = ∠C     ......[Isosceles triangle theorem]

Let ∠A = ∠C = x     ......(i)

In ∆ABC, ∠A + ∠B + ∠C = 180°   ......[Sum of the measures of the angles of a triangle is 180°]

∴ x + 90° + x = 180°     .......[From (i)]

∴ 2x = 90°

∴ x = 90^circ/2    .......[From (i)]

∴ x = 45°

∴ ∠A = ∠C = 45°

∴ ∆ABC is a 45° – 45° – 90° triangle.

∴ AB = BC = 1/sqrt(2) xx "AC"    ......[Side opposite to 45°]

= 1/sqrt(2) xx 5sqrt(2)

∴ AB = BC = 5 units

∴ The height of ∆ABC is 5 units.

Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
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