Need help on geometry question

Question

In ΔABC, ∠A is a right angle and m∠B = 45. If AB = 20 ft, find BC. The options for the question are

•10√3 ft

•20√3 ft

•40 ft

•20√2 ft

Answer 1

Hi Samantha S.

20√2 ft

Given that angle A is a right angle 90°, and angle B is 45° since the angles in a triangle sum to 180°

you have and Isosceles Right Triangle another of the Special Right Triangles you can look up

An Isosceles Triangle has two equal angles and two equal sides

Draw your Isosceles Triangle, use the Pythagorean Theorem to Calculate BC

 

If you draw it correctly AB = AC

BC is the hypotenuse or the side opposite angle A

AB² + AC² = BC²

20² + 20² = BC²

400 + 400 = BC²

800 = BC²

Take the square root of 800 to find BC

√800 = 20√2 = BC