Question

$can \: ya \: all \: please \: help$
In ∆OPQ, right angled at P, OP=7 cm, OQ-PQ=1 cm. Determine the values of sin Q and cos Q.

Answer 1

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Answer 2

Answer:

7/25, 24/25

Step-by-step explanation:

Given, OP = 7 cm, OQ - PQ = 1 cm.   -- (1)

Given that right-angled at P.

In ΔOPQ,

⇒ (OQ)² = (OP)² + (PQ)²

⇒ (OQ)² - (PQ)² =  (7)²

⇒ (OQ + PQ)(OQ - PQ) = 49

⇒ OQ + PQ = 49   ---- (2)

On solving (1) & (2), we get

⇒ OQ - PQ = 1

⇒ OQ + PQ = 49

   --------------------

 2OQ = 50

    OQ = 25 cm.

Substitute OQ = 25 in (i), we get

⇒ OQ - PQ = 1

⇒ 25 - PQ = 1

⇒ PQ = 24 cm.

Now,

∴ Sin Q = OP/OQ = 7/25

∴ Cos Q = PQ/OQ = 24/25

Hope it helps!