# Geometry Homework! i dont understand?

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
asked Feb 2, 2013 in GEOMETRY

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.

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.

• 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

x= 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.

• 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.