Finding Area of Triangle with Trigonometry Word Problems :
Here we are going to see some example problems of finding area of triangle with trigonometry word problems.
Question 1 :
Find the area of a right triangle whose hypotenuse is 10 cm and one of the acute angle is 24° 24'
AC = Hypotenuse side = 10 cm
AB = Opposite side
BC = Adjacent side
Area of triangle = (1/2) ⋅ base ⋅ height
= (1/2) ⋅ BC ⋅ AB
sin θ = AB/AC
sin 24° 24' = AB/10
0.4131 x 10 = AB
AB = 4.131
cos θ = BC/AC
cos 24° 24' = BC/10
0.9107 x 10 = BC
BC = 9.107
= (1/2) ⋅ 9.107 ⋅ 4.131
= 9.107 (2.0655)
= 18.81 cm2
Question 2 :
Find the angle made by a ladder of length 5 m with the ground, if one of its end is 4 m away from the wall and the other end is on the wall.
cos θ = Adjacent side / Hypotenuse side
cos θ = BC / AC
cos θ = 4 / 5
cos θ = 0.8
θ = cos 36° 52'
Question 3 :
In the given figure, HT shows the height of a tree standing vertically. From a point P, the angle of elevation of the top of the tree (that is ∠P ) measures 42° and the distance to the tree is 60 metres. Find the height of the tree.
By finding the length of opposite side, we may find the height of tree.
tan θ = Opposite / Adjacent
tan θ = HT/TP
tan 42 = HT/60
HT = 0.9004 (60)
HT = 54.02 m
Hence the height of the tree is 54.02 m.
After having gone through the stuff given above, we hope that the students would have understood, "Finding Area of Triangle with Trigonometry Word Problems"
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