Question

can anyone tell me the answer of Chapter trigonometry ex:8.1 question 10 and 11??

Answer 1

Hello friend
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10. In Δ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

Answer

Given that, PR + QR = 25 , PQ = 5

Let PR be

x

.  ∴ QR = 25 -

x

By Pythagoras theorem ,

PR

2

 = PQ

2

 + QR

2
x2

 = (5)

2

 + (25 -

x

)

2
x2

 = 25 + 625 + 

x2

 - 50

x

50

x

 = 650

x

 = 13

∴ PR = 13 cm

QR = (25 - 13) cm = 12 cm

sin P = QR/PR = 12/13

cos P = PQ/PR = 5/13

tan P = QR/PQ = 12/5

11.  State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) sec A = 12/5 for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin θ = 4/3 for some angle θ.

Answer

(i) False.

In ΔABC in which ∠B = 90º,

     AB = 3, BC = 4 and AC = 5

Value of tan A = 4/3 which is greater than.

The triangle can be formed with sides equal to 3, 4 and hypotenuse = 5 as

it will follow the Pythagoras theorem.

AC

2

 = AB

2

 + BC

2 

5

2

 = 3

2

 + 4

2

25 = 9 + 16

25

 

=

 

25

(ii) True.

Let a ΔABC in which ∠B = 90º,AC be 12k and AB be 5k, where k is a positive real number.

By Pythagoras theorem we get,

AC

2

 = AB

2

 + BC

2 

(12k)

2

 = (5k)

2

 + BC

2 

BC

2 

+ 25k

2 

= 144k

2

BC

2 

= 119k

2

Such a triangle is possible as it will follow the Pythagoras theorem.

(iii) False.

Abbreviation used for cosecant of angle A is cosec A.cos A is the abbreviation used for cosine of angle A.

(iv) False.

cot A is not the product of cot and A. It is the cotangent of ∠A.

(v) False.

sin θ = Height/Hypotenuse

We know that in a right angled triangle, Hypotenuse is the longest side. 

∴ sin θ will always less than 1 and it can never be 4/3 for any value of θ.

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Hope it helped u