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zhuklara [117]
4 years ago
14

One leg of a right triangle has a length of 77 m. the other sides have lengths that are consecutive integers. find these lengths

.
Mathematics
1 answer:
ANTONII [103]4 years ago
5 0
Let x and x+1 represent the consecutive integers, then x is the other leg and x+1 is the hypotenuse (because the hypotenuse must be greater than its sides).

Use Pythagorean Theorem:
  a²   + b² = c²
(77)² + x² = (x+1)²
5929 + x² = x² + 2x + 1
5928        =        2x
2964        =          x

x+1 = 2965

Answer: The other leg is 2964 m and the hypotenuse is 2965 m
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4 years ago
The triangles below are similar. Triangle A B C. Side A C is 10 and side A B is 5. Angle C is 30 degrees. Triangle D E F. Side E
Gnoma [55]

Answer:

\triangle ABC {\displaystyle \sim } \triangle DE\ F

\triangle CBA {\displaystyle \sim } \triangle FED

\triangle BAC {\displaystyle \sim } \triangle EDF

Step-by-step explanation:

Given

\triangle ABC {\displaystyle \sim } \triangle DE\ F

AC = 10

AB = 5

\angle C = 30^\circ

ED = 7.5

DF = 25

\angle F =30

\angle E =90

Required

Which of the options is/are true:

\triangle CBA {\displaystyle \sim } \triangle FED            \triangle CBA {\displaystyle \sim } \triangle FDE              \triangle BAC {\displaystyle \sim } \triangle EFD

\triangle BAC {\displaystyle \sim } \triangle EDF            \triangle ABC {\displaystyle \sim } \triangle DE\ F             \triangle ABC {\displaystyle \sim } \triangle DFE

The given triangles, implies that:

A {\displaystyle \sim } \ D

B {\displaystyle \sim } \ E

C {\displaystyle \sim } \ F

By taking each sides of both triangle, one after the other; the possible similar triangles are:

\triangle ABC {\displaystyle \sim } \triangle DE\ F

\triangle CBA {\displaystyle \sim } \triangle FED

\triangle BAC {\displaystyle \sim } \triangle EDF

5 0
3 years ago
PLS HELP!!!<br> simplify 3^2 x 3^4 x 3^6= <br> 3^10<br> 3^12<br> 3^0<br> 3^40
EastWind [94]

Answer:

3¹² is answer

Step-by-step explanation:

3^(2+4+6)

3^12

4 0
2 years ago
19. The present age of brother and sister are in the ration 4:5 Before three years the ration of their age was 3:4. find their p
Lyrx [107]

Answer:

Sister = 15 years old

Brother = 12 years old

Step-by-step explanation:

Right now, if the brother is B years old and the sister is S years old, B = (4/5)S because the ratio from brother to sister is 4:5, so if one unit is X, B = 4X and S = 5X

Three years ago, the brother was B-3 years old and the sister was S-3 years old. Keeping one unit as X, we have

B = 3X

S = 4X

B-3 = (3/4)(S-3)

Therefore, we have a system of equations

B = (4/5)S

B-3 = (3/4)(S-3)

Substitute (4/5)S for B into the second equation to only have one variable

(4/5)S - 3 = (3/4)(S-3)

(4/5)S - 3 = (3/4)S - 9/4

add 3 to both sides and subtract (3/4)S from both sides to isolate the variable and its coefficient

(1/20)S = 3/4

multiply both sides by 20 to isolate the S

S = 15

B = (4/5)S = 12

5 0
3 years ago
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