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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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Greg and Erin start at the same point and begin running in different directions. Greg is running east at a speed of 7 miles per
AveGali [126]

Answer: The time at which the distance between the two is 150 miles is 1.3 hr.

Step-by-step explanation:

Step 1: Sketch the problem as shown in the attached image.

The problem can be solved using Pythagoras theorem since the sketch is a right angled triangle.

It follows the equation x² + y² = 15².

The distance covered by Greg is given by <em>x mi</em>, and that of Erin is given by <em>y mi</em>.

Step 2: To derive the distance covered by Erin and Greg, we use the formula <em>Speed = distance ÷ time.</em>

Which by cross-multiplying gives <em>distance = speed × time</em>.

Let time taken to cover the distance be <em>t h</em>.

Given that Speed of Erin is 9 mph and that of Greg is 7 mph.

Hence, distance covered by Greg, x = 7 × t = 7t.

Distance covered by Erin, y = 9 × t = 9t.

Step 3: Insert the terms x and y into the Pythagoras equation x² + y² = 15² and solve for <em>time t.</em>

(7t)² + (9t)² = 15²

49t² + 81t² = 225

(49 + 81)t² = 225

      t² = 225/(49 + 81)

      t² = 225/130

      t² = 1.730769231

       t = √1.730769231

       t = 1.315587029

t = 1.3hr

Hence the time at which the distance between the two is 150 miles is 1.3 hr.

4 0
3 years ago
Write the simplest polynomial function with the zeros..?
zubka84 [21]
All u do is add up until u get ur answer
7 0
3 years ago
Pls help i need this done as quick as possible
Anvisha [2.4K]

Answer:

Infinite Solutions.

Step-by-step explanation:

m+7=3+m+4

Subtract m from both sides:

m+7-m=3+m+4-m

7=3+4

7=7

Both sides are equal.

This means that the value of m does not affect the end result of 7 = 7, which is true. Thus, there are infinite solutions as any value of m will still make the equation true.

4 0
3 years ago
99 POINTS!!! Please help me ASAP!
PilotLPTM [1.2K]

Answer:

F, T, F, T, T, F, F

hope this helps :)

4 0
3 years ago
Find the number of sides when:
svp [43]
((n-2)×180)/n = 156
(n-2)×180=156n
24n =360
n =15

360/n =36
n = 10

a)15 b)10
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3 years ago
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