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Lana71 [14]
3 years ago
6

HELP PLEASE! The distances from a ship to two lighthouses on the shore are 4 miles and 7 miles respectively. If the angle betwee

n the two lines of sight to the lighthouses is 48 degrees. Find the distance between lighthouses?

Mathematics
1 answer:
IrinaK [193]3 years ago
6 0

Answer:

5.25 miles

Step-by-step explanation:

We are required to determine the distance between Lighthouse A and Lighthouse B in the diagram.

Using Law of Cosines

c^2=a^2+b^2-2abCosC\\c^2=7^2+4^2-2(7)(4)Cos48^\circ\\c^2=27.5287\\c=\sqrt{27.5287} \\c=5.25\: miles

The distance between lighthouses is 5.25 miles.

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8 0
3 years ago
Dude is making 12 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $9 per pound and almonds cost $5.25
pshichka [43]

Number of pounds of macadamia nuts is 8 pounds and number of pounds of almonds is 4 pounds.

<u>Step-by-step explanation:</u>

Step 1:

Given total pounds of mixture = 12 pounds, cost of macadamia nuts per pound = $9, cost of almonds per pound = $5.25, total cost of mixture per pound = $7.75.

Let number of pounds of macadamia nuts be x and number of pounds of almonds be 12-x.

Step 2:

Form an equation using the above information.

⇒ 9x + 5.25 (12-x) = 12 × 7.75

⇒ 9x + 63 - 5.25x = 93

⇒ 9x - 5.25x = 30

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Calculate number pounds of almonds

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5 0
2 years ago
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