Question

The base of a 15 foot ladder is 9 feet from a building. The top of the leaning ladder reaches and makes contact with the building’s roof. On the corner of the building, a 6 foot flagpole is erected on the roof. What is the height from the base of the building to the top of the flagpole? Please show your work.

Answer 1

Answer:These are the following dimensions:

1

.

base

=

5

f

t

2

.

hypotenuse

=

15

f

t

3

.

height

=

?

f

t

To solve for the height, use the Pythagorean Theorem, which is:

a

2

+

b

2

=

c

2

where:

a

=

height

b

=

base

c

=

hypotenuse

Substitute your known values into the equation to find the height:

a

2

+

b

2

=

c

2

a

2

+

(

5

)

2

=

(

15

)

2

a

2

+

25

=

225

a

2

=

200

a

=

√

200

a

=

10

√

2

⇒

simplify the radical

a

≈

14.14

f

t

∴

, the ladder goes approximately

14.14

f

t

up the building

Explanation:

Answer 2

9514 1404 393

Answer:

18 feet

Explanation:

The ladder length represents the hypotenuse of a right triangle with a base of 9 and an unknown height (h). We can find that height by using the Pythagorean theorem.

9² +h² = 15²

h² = 225 -81 = 144

h = √144 = 12

So, the ladder extends 12 feet up the side of the building. That is the height of the roof. The top of the flagpole is 6 feet above that, so the top of the flagpole is ...

12 ft + 6 ft = 18 ft

above the ground.

The height to the top of the flagpole is 18 feet.