Question

Isosceles right triangle ABC has a hypotenuse, AB, with a length of 18 feet.

Answer 1

we know that

if ABC is an isosceles right triangle

then

side AC=side BC

angle A=angle B=45 degrees

cos B=adjacent side angle B/hypotenuse

adjacent side angle B=BC

hypotenuse=AB------> 18 ft

angle B=45 degrees

cos 45°=(√2)/2

so

cos 45°=BC/AB-------> solve for BC

BC=AB*cos 45-------> BC=18*(√2)/2------> BC=9√2 ft

AC=BC--------> AC=9√2 ft

the answer part 1) is

the exact lengths of the two sides, AC and BC is

AC=9√2 ft

BC=9√2 ft

Part b) Find the Area of triangle ABC

Area=b*h/2-------> AC*BC/2-----> (9√2)*(9√2)/2--------> 81 ft²

the answer part b) is

the area of triangle ABC is equal to 81 ft²