Geometry Homework! i dont understand?

Question

1. A repairman leans the top of an 18-ft ladder against the top of a stone wall. The base of the ladder is 4-ft from the wall. About how tall is the wall?
2. What type of triangle can Carry make if she has 3 pencils with the lengths of 15, √ ̅207, and 12√ ̅3?
3. What type of triangle can Amelia make if she has 3 crayons with the length of 11, 11, and 11√ ̅3?
4. The hypotenuse of an isosceles right triangle has the length of 24√ ̅2 cm. What is the length of each leg of the triangle

Answer 1

2). The lengths 15, √ ̅207, and 12√ ̅3.

Check by using Pythagorean theorem.

If c² = a² + b², then it is a right angle.

If c² < a² + b², then it is a acute angle.

If c² > a² + b², then it is a obtuse angle.

Here a = 15, b = √ ̅207, and c = 12√ ̅3

a² = (15)² = 225, b² = (√ ̅207)² = 207, and c² = (12√ ̅3)² = 144(3) = 432.

By checking a² + b² = 225 + 207 = 432, c² = (12√ ̅3)² = 144(3) = 432.

a² + b² = c² so, it is a right angle.

Answer 2

3). The lengths 11, 11, and 11√ ̅3.

Check by using Pythagorean theorem.

If c² = a² + b², then it is a right angle.

If c² < a² + b², then it is a acute angle.

If c² > a² + b², then it is a obtuse angle.

Here a = 11, b = 11, and c = 11√ ̅3

a² = (11)² = 121, b² = (11)² = 121, and c² = (11√ ̅3)² = 121(3) = 363.

By checking a² + b² = 121 + 121 = 242, c² = (11√ ̅3)² = 121(3) = 363.

a² + b² < c² so, it is a obtuse angle.

Answer 3

• 1).

From the given data, draw the below figure.

Observe, the figure,

Where,

x = AC = Distance from the top of the ladder to the wall (or)  tall of the wall.

AB = Distance from the bottom of the ladder to the wall = 4 ft.

BC = length of the ladder = 18 ft.

From the pythagorean theorem,

BC² = AB² + AC²

18² = 4² + x²

324 = 16 + x²

x²  = 324 - 16 = 308

x = √308 = 2√77 ft.

Therefore, Distance from the top of the ladder to the wall (or)  tall of the wall is 2√77 ft.

Answer 4

• 4).

An isosceles right triangle has legs of equal length.

From the pythagorean theorem,

c² = a² + b²

Where, a = b, since isosceles and c = hypotenuse.

So,

c² = a² + a²

c² = 2a²

a = √(c²/2)

Substitute c = 24√2 .

a = √((24√2)²/2)

a = 24.

Therefore, length of each leg of the triangle is 24 cm.