Question

ABC is a right triangle ab =bc=3cm
What is the measure of angle a? What is the length of ac

Answer 1

Answer:

measure of angle a is 90°and length of AC is 18

Answer 2

Given: Triangle ABC is a right-angled triangle

AB = BC = 3cm

To Find: The measure of angle A and the length of AC

Solution:

In a right-angled triangle if two sides are equal the triangle is isosceles.

The angles in front of equal sides in an isosceles triangle are also equal.

Here, AB = BC therefore, ∠C = ∠A = x

If angles C and A are equal then angle B must be 90° as there can not be two right angles in a single triangle.

∠A + ∠B + ∠C = 180°                         (Angle sum property)

2x +  90°  = 180°

2x =  90°

x = 45°

So, ∠C = ∠A  = 45°

Since, ∠B  = 90°, the side in front of it must be the hypotenuse

So, AC  is the hypotenuse

According to Pythagoras' Theorem,

(Hypotenuse)²  = (Side1)² + (Side2)²

AC² = AB² + BC²

AC² = 3² + 3²

       = 9 + 9

       = 18

AC = $\sqrt{18}$

     = $\sqrt{(2)(3)(3)}$

     = 3$\sqrt{2}$ cm

Therefore, the measure of angle a is 45° and the length of AC is 3$\sqrt{2}$ cm.