Answer to Question #177204 in Trigonometry for Rainbow_Sparkles

Question #177204

From A, B lies 24 km away on a bearing of 057 and C lies 15km away on a bearing of 347 Find a)The distance between B and C. b)The bearing of B from C.


1
Expert's answer
2021-10-14T07:35:02-0400

a).


If you lay the points on a circle with origin at A, you will get a triangle with an interior angle of 70 deg at A, which is the sum of the bearing of 57 deg between A and B, and 360 deg - 347 deg = 13 deg, the bearing between points A and C. Let 'a' be the side opposite to angle A at point A, you know the distance between A and B call that side c=24km opposite to angle C and side b=15km opposite to angle B.



Using the law of cosines:

"a^2=b^2+c^2-2bc(cosA\\degree)"

"a^2=15^2+24^2-2(15)(24)cos70\\degree"

"a^2=554.745"

"a=23.55km"

Thus, the distance between B and C is BC=23.55km.


b).

From the Law of Sines:

"\\frac{23.55}{sin70\\degree}=\\frac{24}{sinC\\degree}"


"sinC\\degree=\\frac{24*sin70\\degree}{23.55}=\\frac{24*(0.939692621)}{23.55}=0.957648531"


"C=sin^{-1}{(0.957648531)}= 73.265\\degree"


The bearing of B from C is the angle formed by the line joining C and B and rotating about C.

By geometry this angle is :


"180\\degree-(C\\degree +13\\degree)=180\\degree-(73.265\\degree+13\\degree)=93.734\\degree"

Thus, the bearing of B from C is 93.734 deg.

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Comments

Assignment Expert
01.07.21, 00:53

Dear Rainbow_Sparkles, thank you for correcting us.


Rainbow_Sparkles
09.04.21, 19:12

hello, can you explain where you got 8 or 11 because they are not in the question.

Assignment Expert
09.04.21, 17:55

Dear Rainbow_Sparkles, the answer to the question has already published.

Rainbow_Sparkles
03.04.21, 08:35

Welcome, but when will I get my answer

Assignment Expert
31.03.21, 19:35

Dear Rainbow_Sparkles, thank you for clarifying the statement of the question.

Rainbow_Sparkles
31.03.21, 17:20

MUST READ !!!!!!!!! IN b) I meant bearing not meaning

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