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oee [108]
3 years ago
9

A building is 2 ft from a 7 - ft fence that surrounds the property . A worker wants to wash a window in the building 11 ft from

the ground . He plans to place a ladder over the fence so it rests against the building . (See the figure .) He decides he should place the ladder 7 ft from the fence for stability . To the nearest tenth of a foot , how long a ladder will he need ?
Mathematics
1 answer:
White raven [17]3 years ago
3 0

<u>Answer:</u>

The height of the ladder is 14.491 feet

<u>Explanation</u>:

Given the height is 11 feet

Base = 7 + 2 = 9 feet

Consider the ladder to be the hypotenuse

Applying Pythagoras Theorem,  

H^2   = P^2 + B^2

Substituting the values in the above formula,

H^2  = 112 + 92

H^2  = 121 + 81

H^2 = 210

H = sqrt(210)

H = 14.491

Therefore, the height of the ladder is 14.491 feet

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State whether the triangles could be proven congruent, if possible, by SSS or SAS.
Helen [10]

Answer:

1. SSS

2. SAS

3. SAS

4. SSS

5. SAS

6. SAS

Step-by-step explanation:

1) Side FY ≅ Side CW  Given

Side FP ≅ Side CM     Given

Side YP ≅ Side MW    Given

∴ΔMCW ≅ ΔFPY by the Side-Side-Side (SSS) rule of congruency

2) ∠CBD ≅ ∠BCA given that both are alternate interior angles

Side EB ≅ Side EC and Side DB ≅ Side CA Given

ΔBED ≅ ΔAEC by Side-Angle-Side (SAS) rule of congruency

3. ∠SVU ≅ ∠SVT   Given

Side SV ≅ Side SV  by reflexive property

Side VT ≅ Side VU   Given

∴ ΔVSU ≅ ΔVST by Side-Angle-Side (SAS) rule of congruency

4. Side MN ≅ Side QP  Given

Side MQ ≅ Side NP     Given

Side NQ ≅ Side NQ    by reflexive property

∴ΔQNM ≅ ΔQNP by the Side-Side-Side (SSS) rule of congruency

5. Indirect proof

Side GL ≅ Side HL  Given

Side GJ ≅ Side HK     Given

∠JLG ≅ ∠HLK    vertically opposite angles

By sine rule

GJ/sin(∠JLG) = GL/n(∠GJL)

Similarly

HK/sin(∠HLK) = HL/n(∠HKL)

∴ ∠GJL ≅ ∠HKL

∴ ∠LGJ ≅ ∠LHK third angle of two triangles given the other two angles are congruent

∴ΔQNM ≅ ΔQNP by the Side-Angle-Side (SAS) rule of congruency

6. ∠XZY ≅ ∠XZW   Supplementary ∠s with ∠XZY = 90°

Side XZ ≅ Side XZ  by reflexive property

Side ZW ≅ Side ZY   Given

∴ ΔXYZ ≅ ΔXWZ by Side-Angle-Side (SAS) rule of congruency.

3 0
2 years ago
The price of a home is $300,000. After a 10% down payment, the mortgage is $270,000. If this is financed with a 30-year fixed-ra
irinina [24]

Answer:

The correct solution is "$1618.79".

Step-by-step explanation:

The given values are:

Home price,

= $300,000

Down payment,

= 10%

Mortgage,

= $270,000

Rate,

r = 6%

Time,

t = 30 years

As we know,

⇒ PV=P[\frac{1-(1+r)^{-n}}{r} ]

On substituting the values, we get

⇒ 270 000= P[\frac{1-(1+\frac{6}{1200} )^{-12\times 30}}{\frac{6}{1200} } ]

⇒          P=1618.79 ($)

7 0
2 years ago
LOOK AT PICTURE, THEN ANWSER QUESTION, WHOEVER IS CORRECT I WILL MARK BRAINIEST:)
gregori [183]

Answer:

c is the correct answer

5 0
2 years ago
Please help, I’m new to this app so O
umka2103 [35]

Answer:

x=10 5x=50 2x=20

Step-by-step explanation:

5x+2x+110=180

180-110=70

7x=70

x=10

5*10=50

2*10=20

5 0
2 years ago
Malik had two tests on Wednesday. On the science test, each question was worth 4 points. On the math test, each question was wor
Gre4nikov [31]

Answer:

Science Test

Step-by-step explanation:

If he missed 12 points on each test (-12) he missed 2 questions on the math test and 4 questions on the sceince test.

7 0
2 years ago
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