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hodyreva [135]
3 years ago
7

Island A is 150 miles from island B. A ship captain travels 240 miles from island A and then finds that he is off course and 200

miles from island B. What bearing should he turn to, so he is heading straight towards island B?
Mathematics
1 answer:
Stells [14]3 years ago
4 0
We know that
Applying the law of cosines: 

<span>c</span>²<span> = a</span>²<span> + b</span>²<span> - 2abcos(C) </span>
<span>where: </span>
<span>a,b and c are sides of the triangle and C is the angle opposite side c </span>

<span>that is </span>
<span>150</span>²<span> = 240</span>²<span> + 200</span>²<span> - 2(240)(200)cos(C) </span>

<span>solve for C </span>

<span>22,500 = 57,600 + 40,000 - 96,000cos(C) </span>
<span>22,500-57,600-40,000 = -96,000cos(C) 
</span>-75,100=-96,000cos (C)
cos (C)=0.7822916
C=arc cos(0.7822916)--------> C=38.53°°

<span>hence, </span>
<span>he should turn in the direction of island b by
180 - 38.53 </span><span>= 141.47 degrees</span>
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an example would be 3,4,5

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17. Classify Each Angle Pair then find the value of X
IRISSAK [1]

<u>Given</u> -

  • If l || m, m∠1 = (13x + 24)°, and m∠2 = (5x-6)°,

<u>To find</u> -

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<u>Concept</u> -

Whenever two parallel lines are cut by a transversal, an interesting relationship exists between the two interior angles on the same side of the transversal. These two interior angles are supplementary angles. Hence, according to the figure l and m are two parallel lines and t is the transversal intersecting them then ∠1 + ∠2 = 180°.

<u>Solution</u> -

\rightarrow\sf{(13x+24)^{ \circ}+(5x-6)^{ \circ}=180^{ \circ}}

\rightarrow\sf{13x+5x+24-6=180}

\rightarrow\sf{18x+18=180}

\rightarrow\sf{18x+18=180}

\rightarrow\sf{18(x+1)=180}

\rightarrow\sf{x+1=\frac{180}{18}}

\rightarrow\sf{x+1=10}

\rightarrow\sf{x=10-1}

\rightarrow\boxed{\bf{x=9}}

m∠2 = (5x-6)° = {5(9) - 6}° = {45 - 6}°= 39°

Henceforth, m∠2 = 39°

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