Question

In triangle PQR if angle Q = 90 degree and sin R = 3/5 then find the value of cos p

Answer 1

Answer: cos p = 3/5

explanation:-

sin R = opposite side/ hypotnuse side = 3/5

cos p = adjacent side/ hypotnuse side = 3/5

Answer 2

The value of cos  P is 3 / 5.

Given: If in a triangle PQR, right-angled at Q, sin R = 3 / 5.

To Find: The value of cos P.

Solution:

• We know that in a right-angled triangle, there is a base, a perpendicular, and a hypotenuse concerning the angle which is equal to 90°.

• Accordingly, we can say that;

           tan A = Perpendicular / Base                                          ...(1)

            sin A = Perpendicular / Hypotenuse                             ...(2)

           cos A = Base / Hypotenuse                                            ...(3)

• The Pythagoras theorem states that;

           ( Hypotenuse )² = ( Perpendicular )² + ( Base )²             ...(4)

Coming to the numerical, we are given;

Δ PQR is right-angled at Q,

            sin R = 3 / 5 = Perpendicular / Hypotenuse        

So, we can say that,

The perpendicular concerning ∠R = 3 units

The hypotenuse concerning ∠R = 5 units

So, we can find the hypotenuse from (4),

             ( Hypotenuse )² = ( Perpendicular )² + ( Base )²    

         ⇒ ( 5 )² = ( 3 )² + ( Base )²    

         ⇒ ( Base )² = 25 - 9

         ⇒ ( Base ) = √16

                           = 4 units

So, we need to find the cosine of ∠P. So, the base and perpendicular gets interchanged.

So, the perpendicular concerning ∠P = 4 units

The hypotenuse concerning ∠P = 5 units

The base concerning ∠P = 3 units

So, putting respective values in (3), we get;

                cos  P = Base / Hypotenuse  

            ⇒ cos  P = 3 / 5

Hence, the value of cos  P is 3 / 5.

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