Answer:
see below
Explanation:
Answer 1:-
here we need to find out the values of b and c .
in a right angled triangle,
sinθ = p/h
sin34° = c/20
0.56 = c/20
c = 0.56*20
c = 11.2
again,
cosθ = b/h
cos34° = b/20
0.83 = b/20
b = 20*0.83
b = 16.6
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Answer 2:-
here we need to find out the values of a , c and measure of angle C .
in a right angled triangle,
sinθ = p/h
sin68° = a/18
0.93 = a/18
a = 18*0.93
a = 16.74 ≈ 16.7
again,
cosθ = b/h
cos68° = c/18
0.37 = c/18
c = 18*0.37
c = 6.66 ≈ 6.7
we know that the angle sum property of a ∆ is 180° .So ,
90° + 68° + m(C) = 180°
m(C) = 180° - 158°
m(C) = 22°
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Answer 3:-
in a right angled triangle,
cosθ = base/hypotenuse
in the given ∆ ,
b = 24
h = 74
So ,
cosA = 24/74
cosA = 12/37
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Answer 4:-
in a right angled triangle,
sinθ = perpendicular/hypotenuse
in the given ∆ ,
h = 85
p = 13 ,
Therefore,
sinB = 13/85
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Answer 5:-
in a right angled triangle,
hypotenuse ² = base² + perpendicular ²
So that ,
14² = 11² + x²
196 = 121 + x²
196 - 121 = x²
75 = x²
√75 = x
8.66 = x
since here 8.66 is not an integer, therefore the sides do not form a Pythagorean triplet .
and we are done!