Notifications
Clear all
Applications of Trigonometry
1
Posts
2
Users
1
Likes
200
Views
0
16/06/2021 11:59 am
Topic starter
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
1 Answer
1
16/06/2021 12:02 pm
Using given instructions, draw a figure. Let AC be the broken part of the tree. Angle C = 30°
BC = 8 m
To Find: Height of the tree, which is AB
From figure: Total height of the tree is the sum of AB and AC i.e. AB +AC
In right ΔABC,
Using Cosine and tangent angles,
cos 30° = BC/AC
We know that, cos 30° = √3/2
√3/2 = 8/AC
AC = 16/√3 …(1)
tan 30° = AB/BC
1/√3 = AB/8
AB = 8/√3 ….(2)
Therefore, total height of the tree
= AB + AC = 16/√3 + 8/√3
= 24/√3
= 8√3 m.