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svet-max [94.6K]
4 years ago
8

Solve the right triangle. Round decimal answers to the nearest tenth.​

Mathematics
2 answers:
Sergeu [11.5K]4 years ago
7 0

Answer:

DE ≈16.1; m∠E ≈ 60.3°; M∠D ≈ 29.7°

Step-by-step explanation:

1) DE

DE² = DF² + EF² = 14² +8² = 196 + 64 = 260

DE =√26 ≈ 16.1

2) m∠E

sin E = DF/DE = 14/16.1 ≈ 0.8682

m∠E = arcsin 0.8682 ≈ 60.3°

3) m∠D

\begin{array}{rcl}m\angle D +  m\angle E + m\angle F & = & 180^{\circ}\\m\angle D +  60.3^{\circ} + 90^{\circ} & = & 180^{\circ}\\m\angle D +  150.3^{\circ} & = & 180^{\circ}\\m\angle D & = & \mathbf{29.7^{\circ}}\\\end{array}

Arada [10]4 years ago
5 0

Answer:

DE = sqrt(8^2+14^2) = ~16.1

E = arctan(14/8) = 60.3

D= arctan(8/14) =29.7

Step-by-step explanation:

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Measurement is the use of numbers according to a standard true or false
Softa [21]

Answer:

True

Step-by-step explanation:

3 0
3 years ago
Finding perimeter and area.
Aleks04 [339]

Answer:

1. P = 14cm; A = 10cm^2

2. P = 24cm; A = 12cm^2

3. P = 32cm; A = 63cm^2

4. P = 36cm; A = 80cm^2

5. P = 32cm; A = 60cm^2

6. P = 36cm; A = 81cm^2

7. P = 26cm: A = 30cm^2

8. P = 28cm; A = 49cm^2

9. P = 26cm: A = 42cm^2

Step-by-step explanation:

Formula to find perimeter for a rectangle:

length + width + length + width

l + w + l + w

Formula to find area for a rectangle:

length × width

l × w

1.

Perimeter (P): 5 + 2 + 5 + 2 = 14

Area (A): 5 × 2 = 10

2.

P: 6 + 2 + 6 + 2 = 24

A: 6 × 2 = 12

3.

P: 7 + 9 + 7 + 9 = 32

A: 7 × 9 = 63

4.

P: 10 + 8 + 10 + 8 = 36

A: 10 × 8 = 80

5.

P: 10 + 6 + 10 + 6 = 32

A: 10 × 6 = 60

6.

P: 9 + 9 + 9 + 9 = 36

A: 9 × 9 = 81

7.

P: 10 + 3 + 10 + 3 = 26

A: 10 × 3 = 30

8.

P: 7 + 7 + 7 + 7 = 28

A: 7 × 7 = 49

9.

P: 6 + 7 + 6 + 7 = 26

A: 6 × 7 = 42

Area will always have its units squared (cm^2) because the formula requires we multiply the numbers and therefore the units: cm × cm = cm^2

4 0
3 years ago
Help please I don’t know the answer
andrew-mc [135]

Answer:

$16,534.95

Step-by-step explanation:

To compute interest on loans, we use the compounded interest equation. We use the equation A=P(1+\frac{r}{n})^{nt} where

  • P is the principle or starting value
  • A is the total amount after interest and a period of time
  • r is the rate at which interest gathers as a decimal
  • t the time in years
  • n is the number of times compounded in a year.

For this problem, we know P=$8000, r=19%=0.19, t=4 years and n=2. We substitute into the formula and simplify to find the total amount A.

A=P(1+\frac{r}{n})^{nt}\\A=8000(1+\frac{0.19}{2})^{2(4)}\\A=8000(1+0.095)^{8}\\A=16,534.95

8 0
4 years ago
Which set of side lengths defines a right triangle?
Snowcat [4.5K]
In a right triangle, the square of the largest side is equal to the sum of the squares of the smaller sides, so if you plug the sides in to that equation, you should get zero if those sides form a right triangle.
B is the only option where this is true, so I believe set B defines a right triangle.
4 0
3 years ago
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Marcel is purchasing a board to build a bookcase. He wants to divide the board into 1.75 foot sections . He need six sections .
FromTheMoon [43]
10.5 feet (1.75x6) hope I helped
8 0
3 years ago
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