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3 years ago

15

Amy and her sister are making lemonade for the school dance. Their recipe makes 2 quarts of lemonade. If they make 35 times the

recipe, how many gallons of lemonade will Amy and her sister have?

1 answer:

Anastaziya [24]3 years ago

7 0

Its 17.5 gallons because 2 quarts times 35 equals 70 quarts and 17.5 gallons equals 70 quarts

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1. In a recent wind storm a large tree broke and made a 58° angle

yKpoI14uk [10]

*see attachement for diagram

Answer:

40.4 ft

Step-by-step explanation:

Let the part that broke away be represented as "x"

Thus, the digram makes a right triangle shape.

The closest total length of tree before the storm = x + 14 ft

Apply trigonometric function to find x.

Reference angle = 58°

Side adjacent to reference angle = 14 ft

Hypotenuse = x

Apply CAH, which is:

Cos 58 = adj/hyp

Cos 58 = 14/x

x * Cos 58 = 14

x = 14/Cos 58

x = 26.4191188 ≈ 26.4 ft

✔️closest total length of tree before the storm = x + 14 ft = 26.4 + 14 = 40.4 ft

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Solve ABC <br>c=10, B=35°, C=65%

NISA [10]

Answer:

Part 1) The measure of angle A is $A=80\°$

Part 2) The length side of a is equal to $a=10.9\ units$

Part 3) The length side of b is equal to $b=6.3\ units$

Step-by-step explanation:

step 1

Find the measure of angle A

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

$A+B+C=180\°$

substitute the given values

$A+35\°+65\°=180\°$

$A+100\°=180\°$

$A=180\°-100\°=80\°$

step 2

Find the length of side a

Applying the law of sines

$\frac{a}{sin(A)}=\frac{c}{sin(C)}$

substitute the given values

$\frac{a}{sin(80\°)}=\frac{10}{sin(65\°)}$

$a=\frac{10}{sin(65\°)}(sin(80\°))$

$a=10.9\ units$

step 3

Find the length of side b

Applying the law of sines

$\frac{b}{sin(B)}=\frac{c}{sin(C)}$

substitute the given values

$\frac{b}{sin(35\°)}=\frac{10}{sin(65\°)}$

$b=\frac{10}{sin(65\°)}(sin(35\°))$

$b=6.3\ units$

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