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The diagram shows the position
of three towns represented by
letters A, B and C.
NA
B is 7 km from A on a bearing of 037°
C is 8 km from B on a bearing of 140°
Find the bearing of C from A.
Give your answer correct to 1 decimal place.

The Diagram Shows The Position Of Three Towns Represented By Letters A B And C NA B Is 7 Km From A On A Bearing Of 037 C Is 8 Km From B On A Bearing Of 140 Find class=

Sagot :

Answer:

Step-by-step explanation:

143º I’m not sure

The bearing of town C from town A is 93.3 degree if the B is 7 km from A on a bearing of 037° C is 8 km from B on a bearing of 140°

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

If we extend the line NA and NB

As we can see, line NA and NB are parallel and cut by transversal AB

The angle NBA and BAN' will be equal.

Angle BAN' = 180 - 37 = 143 degree = angle NBA

Angle CBA = 360 - 140 - 143

Angle CBA = 77 degree

Now, applying cos law:

b² = a² + c² - 2ac[cos B]

b² = (8)² + (7)² - 2(8 x 7 x cos77)

b = 9.37 km

To find the measure of the angle A applying sin law:

(sinA)/a = (sinB)/b

sinA = (axsinB)/b

sinA = (8xsin77)/9.37

A = 56.3⁰

Bearing of town C from town A:

α = A + 37⁰

α = 56.3⁰ + 37⁰

α = 93.3⁰

Thus, the bearing of town C from town A is 93.3 degree if the B is 7 km from A on a bearing of 037° C is 8 km from B on a bearing of 140°

Learn more about the angle here:

brainly.com/question/7116550

#SPJ2

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