Answer:
Value of h is 4.5 unit.
Step-by-step explanation:
Given:
MO = 12 and PO = 2
∠N and ∠p are right angle
To find: Value of h.
In ΔMNO and ΔONP
∠MNO = ∠OPN = 90°
∠MON = ∠NOP ( common angle)
⇒ ΔMNO and ΔONP are similar triangle by AA Similiarity criteria.
Corresponding part of similar triangles are ,
∠OMN = ∠ONP
[tex]\frac{OM}{ON}=\frac{MN}{PN}=\frac{ON}{OP}[/tex]
Consider,
[tex]\frac{OM}{ON}=\frac{ON}{OP}[/tex]
[tex]OM\times OP=ON^2[/tex] .................(1)
Now in ΔONP,
using Pythagoras Theorem
ON² = NP² + OP²
ON² = h² + 2²
ON² = h² + 4 .............(2)
From (1) and (2), we have
12 × 2 = h² + 4
h² = 24 - 4
h² = 20
[tex]h=\sqrt{20}[/tex]
[tex]h=2\sqrt{5}[/tex]
h = 2 × 2.236 ( Value of √5 is 2.236 )
h = 4.472
h = 4.5 unit
Therefore, Value of h is 4.5 unit.
