Respuesta :
Answer:
51.2
Step-by-step explanation:
Sin^{-1}(((51*(sin(78)))/64)) = 51.2
The angle between the running and skateboarding paths is 51.2 degrees.
What is a triangle?
'A triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.'
According to the given problem,
Side A = 51 meters
Side B = 64 meters
Given, angle = 78°
We know, according to the law of sines,
[tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex]
⇒ [tex]\frac{51}{sinA}=\frac{64}{sin78}[/tex]
⇒ [tex]\frac{sinA}{51} = \frac{sin78}{64}[/tex]
⇒ sin A = [tex]\frac{51*sin78}{64}[/tex]
⇒ sinA = 0.78
⇒ A = [tex]sin^{-1} (0.78)[/tex]
⇒ A = 51.2°
Hence, we can conclude, the angle between the running and skateboarding paths is 51.2 degrees.
Learn more about triangles here: https://brainly.com/question/2773823
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