Question

Construct an isosceles triangle ABC in which AB=AC = 9 cm and BÂC = 45°. Measure ABC and BC​

Answer 1

m∠ABC = 67.5°

BC = =6.888301782572 cm

Explanation:

ABC is an isosceles triangle

Then

m∠ABC = m∠ACB

The sum of the interior angles of a triangle is equal to 180°

Then

m∠ABC + m∠ACB + m∠BAC = 180°

Then

m∠ABC + m∠ACB + 45 = 180°

Then

2 × m∠ABC = 180°

Then

m∠ABC = (180−45)÷ 2 = 67.5°

Law of SIN :

`(9)/(\sin \left( 67.5\right) ) =(BC)/(\sin \left( 45\right) )`

`BC=(9)/(\sin \left( 67.5\right) ) * \sin \left( 45\right) ==6.888301782572`