Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,459 questions

17,854 answers

1,446 comments

809,567 users

Geometry Homework! i dont understand?

+2 votes
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 by anonymous Apprentice

4 Answers

+2 votes

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.

answered Feb 2, 2013 by richardson Scholar
+2 votes

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.

answered Feb 2, 2013 by richardson Scholar
0 votes
  • 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.

answered Jun 27, 2014 by lilly Expert
0 votes
  • 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.

answered Jun 27, 2014 by lilly Expert

Related questions

asked Mar 20, 2016 in PRECALCULUS by anonymous
asked Feb 22, 2016 in PRECALCULUS by anonymous
asked Feb 22, 2016 in PRECALCULUS by anonymous
asked Nov 2, 2013 in GEOMETRY by futai Scholar
...