Answer:
The size of angle SPQ is 52.4 degrees.
Step-by-step explanation:
Given:
Two coast guard station and a ship at a point from these coast guard.
That makes,three side length of a triangle.
Length of PQ = [tex]25[/tex] km
Length of PS =[tex]18[/tex] km
Length of QS = [tex]20[/tex] km
We have to find the measure of angle SPQ.
Let the measure of SPQ be 'P'.
Using cosine law:
⇒ [tex]p^2=q^2+s^2-2qs\times cos(P)[/tex]
⇒ Plugging the values.
⇒ [tex]20^2=18^2+25^2-2\times 18\times 25\times cos (P)[/tex]
⇒ [tex]400=324+625-900\times cos (P)[/tex]
⇒ [tex]400=949-900\times cos (P)[/tex]
⇒ [tex]400-949=-900\times cos(P)[/tex] ...subtracting 949 both sides.
⇒ [tex]-549=-900\times cos(P)[/tex]
⇒ [tex]\frac{-549}{-900}= cos(P)[/tex] ...dividing -900 both sides.
⇒ [tex]0.61=cos(P)[/tex]
⇒ [tex]cos^-^1(0.61)=P[/tex]
⇒ [tex]P=52.4[/tex] degrees
The size of angle SPQ = 52.4 degrees.
