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borishaifa [10]
3 years ago
6

Find the missing length. The triangles are similar.

Mathematics
1 answer:
hodyreva [135]3 years ago
8 0

Answer:

182

Step-by-step explanation:

First, we can say that ∠ACB and ∠BCF are opposite angles because they are not next to each other and are formed by intersecting lines. Therefore, ∠ACB = ∠BCF

Next, angles correspond with the side opposite of it. This means that, for example, ∠ACB corresponds with line AB and ∠BCF corresponds with line BF. Because ∠ACB and ∠BCF are equal and the triangles are similar, we can say that their corresponding sides have a ratio with each other. Similarly, ∠CAB corresponds to CB, ∠ABC corresponds to AC, ∠CWV corresponds to CV, and ∠CVW corresponds to CB.

Because the triangle CVW is isosceles, we can say that the angles whose corresponding sides are equal are equal as well, so ∠CAB = ∠ABC and ∠CVW = ∠CVW. Next, because ∠ACB and ∠BCF are equal and correspond to each other, and the other two angles in each triangle are equal to each other, we can say that the other two angles must be equal. Another way of putting this is like this:

Say that x = ∠CAB. Then,

∠CAB + ∠ABC + ∠ACB = 180

x + x + ∠ACB = 180

2x + ∠ACB = 180

subtract ∠ACB from both sides

180 - ∠ACB = 2x

Similarly, if y = ∠CWV,

180 - ∠WCV = 2y. Therefore, 2y=2x and y=x, so ∠CAB = ∠ABC = ∠CWV = ∠CVW.

Given this, we can say that sides CV and CW correspond with BC and AC. This means that the ratio between, for example, CV and BC is equal to the ratio between CW and AC. Therefore,

CV/BC = CW/AC

84/182 = 84/?

Filling in the blank, 84/182 is equal to 84/182, so ? = 182

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Answer:

15

Step-by-step explanation:

Co-efficient = number multiplied by a variable

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4 0
1 year ago
Ali was swimming along the bottom of his backyard pool at a depth of 6 feet then he pushed off the bottom and rose 4 feet what i
olga nikolaevna [1]

Answer:

2 feets

Step-by-step explanation:

Given that :

Alli's Initial depth = 6 feets

Number of feets in which Alli rose = 4 feets

Alli's new position relative to the surface of the pool:

Difference of Alli's initial depth and feets risen :

6 feets - 4 feets = 2 feets

Hence, Alli is now 2 feets below the surface of the pool.

7 0
3 years ago
I’m confused on this one
Mandarinka [93]

Remark

If the lines are parallel then triangle RQS will be similar to triangle RTP


From that, all three lines in one triangle will bear the same ratio to all three lines of the second triangle.


Givens

PQ = 8

QR = 5

RS = 15

ST = x + 3


Ratio

QR/RP = RS/RT


Sub and solve

RP = 5 + 8

RP = 13


RT = 15 + x + 3

RT = 18 + x


5/13 = 15 / (18 + x) Cross multiply

5(18 + x) = 195 Remove the brackets on the left.

90 + 5x = 195 Subtract 90 from both sides.

5x = 105 Divide by 5

x = 105/5

x = 21 Answer <<<<<<<

3 0
3 years ago
Pls Help! John wants to prove ABC = to DEF. He Knoes AB = DE and AC = DF. With Screenshot
matrenka [14]

Answer:

\angle A \cong \angle D

Step-by-step explanation:

The Side-Angle-Side method cana only be used when information given shows that an included angle which is between two sides of a ∆, as well as the two sides of the ∆ are congruent to the included side and two sides of the other ∆.

Thus, since John already knows that \overline{AB} \cong \overline{DE} and \overline{AC} \cong \overline{DF}, therefore, an additional information showing that the angle between \overline{AB} and \overline{DE} in ∆ABC is congruent to the angle between \overline{AC} and \overline{DF} in ∆DEF.

For John to prove that ∆ABC is congruent to ∆DEF using the Side-Angle-Side method, the additional information needed would be \angle A \cong \angle D.

See attachment for the diagram that has been drawn with the necessary information needed for John to prove that ∆ABC is congruent to ∆DEF.

7 0
2 years ago
11. John puts a fence around his rectangular backyard. The width of his backyard is 10 feet. He
Lady_Fox [76]

Length = 20 ft

If he uses 60 ft of fencing to line his rectangular backyard, then the perimeter is 60 ft.

Perimeter formula is ((Width × 2) + (Length × 2))

10 × 2 = 20

20 × 2 = 40

40 + 20 = 60

4 0
2 years ago
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