Question

In a triangle PQR with right angle at Q, the value of ∠P is x, PQ = 7 cm and QR = 24 cm, then find sin x and cos x.

Answer 1

sinX=24/25 and cosX=7/25

Answer 2

Given:-

In a triangle PQR with right angle at Q, the value of ∠P is x, PQ = 7 cm and QR = 24 cm, then find sin x and cos x.

Solution:-

Given BC + CA = 23 cm ------------- (Eq 1)

BC - CA = 7 cm ---------------- (Eq 2)

Adding Eq 1 + 2

$\large\ \: BC + CA = 23 \\ \large\frac{ BC - CA = 7}{⇒ \: 2BC = \: 30}$

$\large\ ⇒ 2BC = 30$

$\large\ ⇒ BC = \frac{20}{2}$

$\large\ ⇒ BC = 15.$

Substitute 'BC' value in Eq 1

$\large\ ⇒ BC + CA = 23$

$\large\ ⇒ BC = 15$

$\large\ ⇒ 15 + CA = 23$

$\large\ ⇒ CA = 23 - 15$

$\large\ ⇒ CA = 8$

By Using Ppythagoras theorem

$\large\ ⇒ (side)² + (side)² = (hyp)²$

$\large\ ⇒ (AC)² + (BC)² = (AB)²$

$\large\ ⇒ (8)² + (15)² = (AB)²$

$\large\ ⇒ 64 + 225 = (AB)²$

$\large\ ⇒ 289 = (AB)²$

$\large\ ⇒ AB = \sqrt{289}$

$\Large{\boxed{AB = 17 cm.}}$

∴ Hence, AB = 17 cm.