Question

Two coastguard station,Pand Q,are 25 km apart,Q is due east of P.A ship ,is at a distance of 18 km from P and 20km from Q.Calculate the size of angle SPQ

Answer 1

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 = $25$ km

Length of  PS =$18$ km

Length of QS = $20$ km

We have to find the measure of angle SPQ.

Let the measure of SPQ be 'P'.

Using cosine law:

⇒ $p^2=q^2+s^2-2qs\times cos(P)$

⇒ Plugging the values.

⇒ $20^2=18^2+25^2-2\times 18\times 25\times cos (P)$

⇒ $400=324+625-900\times cos (P)$

⇒ $400=949-900\times cos (P)$

⇒ $400-949=-900\times cos(P)$  ...subtracting 949 both sides.

⇒ $-549=-900\times cos(P)$

⇒ $\frac{-549}{-900}= cos(P)$                     ...dividing -900 both sides.

⇒ $0.61=cos(P)$

⇒ $cos^-^1(0.61)=P$

⇒ $P=52.4$ degrees

The size of angle SPQ = 52.4 degrees.