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Answers
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Step-by-step explanation:
Given :-
In ∆ MNK , <M = 60° , <N = 90° and MN = 5cm
To find :-
Find MK ?
Solution :-
Given that
In ∆ MNK , <M = 60° , <N = 90° and MN = 5cm
We know that
By Angle Sum Property
=> <M + <N + <K = 180°
=> 60°+90°+ <K = 180°
=> 150°+ <K = 180°
=> <K = 180°-150°
=> <K = 30°
We know that
Cos A = Adjacent side to A / Hypotenuse
=> Cos (<NMK) = MN/MK
=> Cos 60° = 5/MK
=> 1/2 = 5/MK
On applying cross multiplication then
=> 1×MK = 2×5
=> MK = 10 cm
Therefore, MK = 10 cm
(or)
Sin A = Opposite side to A / Hypotenuse
=> Sin 30° = MN / MK
=> 1/2 = 5/MK
On applying cross multiplication then
=> 1×MK = 2×5
=> MK = 10 cm
Therefore, MK = 10 cm
Answer:-
The measure of the linesegment MK = 10 cm
Used formulae:-
Angle Sum Property:-
The sum of all the three interior angles in a triangle is 180°.
→ Sin A = Opposite side to A / Hypotenuse
→ Cos A = Adjacent side to A / Hypotenuse
→ Sin 30° = 1/2
→ Cos 60° = 1/2
