2022 Two Straight Roads Intersect At Point P And Make And Angle Of 43\Xb0 There. At Point Q On, One Road Is A Building That Is 365 M From P And At Poi

• Two straight roads intersect at point P and make and angle of 43° there. At point Q on

one road is a building that is 365 m from P and at point R on the other road is a building
that is 462 m from P. Find the direct distance from Q to R.

 

Answer:

The direct distance between Q and R is 317 meters.

Step-by-step explanation:

Use the Law of Cosine:

c² = a² + b² - 2abCosC

Where:

a = PQ =  365 m

b = PR = 462 m

C = 43° ⇒ 0.73  (Use a scical to find the value of Cos 43)

c = QR = distance between the two buildings at Points Q and R

Substitute:

c² = (365)² + (462)² - 2(365)(462)(0.73)

c² = 133,225 + 213,444 - 246,199.8

c² = 100,469.2  or  100,470

c ≈ √ 100,470

c ≈ 316.96 or 317 meters

The direct distance between Q and R is 317 meters.


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