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mihalych1998 [28]
1 year ago
10

Find the number of distinct triangles with the measurements a = 8, b = 14, and A = 30°.​

Mathematics
1 answer:
Maslowich1 year ago
5 0

Answer: 2

Step-by-step explanation:

By the law of sines,

\frac{\sin B}{b}=\frac{\sin A}{a} \\ \\ \frac{\sin B}{14}=\frac{\sin 30^{\circ}}{8} \\ \\ \frac{\sin B}{14}=\frac{1}{16} \\ \\ \sin B=\frac{14}{16} \\ \\ B=\sin^{-1} \left(\frac{14}{16} \right), 180^{\circ}-\sin^{-1} \left(\frac{14}{16} \right) \\ \\ B \approx 61.04^{\circ}, 118.96^{\circ}

Since either of these values for B will form a triangle (as A+B will be less than 180 degrees), 2 triangles can be formed with these measurements.

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laila [671]

Answer:

y = -10

Step-by-step explanation:

(-7x+3y) - (-7x +10y) =-65 -(-135)

-7x + 3y + 7x -10y = 70

-7y = 70

y = -10

7 0
3 years ago
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A circular pool if filling with water. Assuming the water level will be 4' deep and the diameter is 20' , what is the volume of
Yuliya22 [10]

35,569.92 L of water is required to fill the pool

Step-by-step explanation:

  • Step 1: Find the area of the circular pool when radius = 20/2 = 10 ft

⇒ Area = πr² = 3.14 × 10² = 314 ft²

  • Step 2: Find the volume of the pool

Volume = Area × Depth

             = 314 × 4 = 1256 ft³

  • Step 3: Convert the volume into liters.

Volume of water = 1256 × 28.32 = 35,569.92 L (∵1 ft³ = 28.32 L)

8 0
3 years ago
Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owne
MrRissso [65]

The age of the van owned = 12 years

The age of the truck owned  = 29 years

Step-by-step explanation:

Here, the given question is INCOMPLETE.

Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owned the truck for 17 years longer than she has owned the van. If the sum of the ages of the vehicles is 41 years, how old is the van and how old is the truck?

Let us assume the number of years Laura has owned the van = S years

So, according to the question:

The number of years she has owned truck = S + 17 years

Now, Sum of the age of ( Truck + Van)  = 41 years

⇒ (S + 17 years) + (S years)  = 41 years

or, 2 S +  17 = 41

or, 2 S  = 4 1 -1 7 = 24

or, S  = 24/2 = 12 years

or, S  = 12 years

Hence the age of the van owned = 12 years

The age of the truck owned  = S  + 17  = 12 + 17 = 29 years

6 0
3 years ago
PLEASE HELP ME, I HAVE BEEN WAITING FOR A DAAYY!! How old am i if 400 reduced by 3 times my age is 244?
Vlad1618 [11]

Answer:

52 years

Step-by-step explanation:

Let

Your age = x

3 times your age = 3 * x

= 3x

The equation can be written as:

400 - 3x = 244

400 - 244 = 3x

156 = 3x

Divide both sides by 3

x = 156/3

x = 52

Therefore,

Your age is 52 years

4 0
2 years ago
Hey! i’ll give brainliest please help
NeTakaya

Answer:

a mans car...

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a man's car breaks down while driving to work

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