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State True or False.
In ∆ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. The values of sin P = $513$ ,
cos P = $1213$ and tan P = $512$ .

see full answer

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True

False

answer is A.

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Detailed Solution

Given that in ∆ PQR, right-angled at Q,
PR + QR = 25 cm ……(1)
and PQ = 5 cm.
We know that according to Pythagoras theorem,

h y p o t e n u s e 2 = b a s e 2 + p e r p e n d i c u l a r 2

In ∆ PQR, it is given that it is right angled at Q, so the hypotenuse is PR.

⇒ P R 2 = P Q 2 + Q R 2

⇒ P Q 2 = P R 2 − Q R 2

Given that QR + PR = 25,

⇒

25 = (PR + QR)(PR – QR)

⇒

PR – QR = 1 ……(2)
Add equation(1) and (2) for PR and QR.
We get,

⇒

PR + QR +PR – QR = 25+1

⇒

2PR = 26

⇒

PR = 13
Substitute PR in equation (2).

⇒

13 – QR = 1

⇒

QR = 12
So, PR= 13cm and PQ = 12cm.
Triangle PQR can depicted as,
Question Image

The values of sinP, cosP and tanP are,

sin P = P H = Q R P R sin P = 513 cos P = B H = P Q P R cos p = 1213 tan P = P B = Q R P Q tan P = 512

Hence the statement is true i.e, the values are sin P=

513

, cos P =

1213

and tan P =

512

.
Therefore, the correct option is 1.

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