Question

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

Find the exact lengths of the other two sides, AC and BC.

AC =
a0√
a1 feet

BC =
a2√
a3 feet

To the nearest square foot, find the area of ABC .

Area of ABC =
a4 square feet

Answer 1

The exact lengths of the two legs AC and BC of an isosceles right triangle with a hypotenuse of 18 feet are 9√2 feet each. Using the Pythagorean theorem, we calculate the area of the triangle to be 81 square feet when rounded to the nearest square foot.

Step-by-step explanation:

To find the lengths of the other two sides, AC and BC, of isosceles right triangle ABC with hypotenuse AB of length 18 feet, we employ the Pythagorean theorem. Since triangle ABC is an isosceles right triangle, sides AC and BC are equal, and we can denote their lengths as 'x'. Applying the theorem, we have:

x² + x² = 18²

2x² = 18²

x² = (18²) / 2

x² = 324 / 2

x² = 162

x = √162

x = 9√2 feet

The exact lengths of both AC and BC are 9√2 feet.

To calculate the area of triangle ABC, we use the formula for area of a right triangle, which is (base * height) / 2. In this case, base and height are equal (AC = BC), so it simplifies to:

Area = (AC * AC) / 2

Area = (9√2 * 9√2) / 2

Area = (81 * 2) / 2

Area = 162 / 2

Area = 81 square feet

To the nearest square foot, the area of triangle ABC is 81 square feet.

Answer 2

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