Applications of trigonometry

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A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of 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.
First, Using given instructions, draw a figure. Let AC be the broken part of the tree.
Next solve: Angel C = 30 degrees. BC = 8mTo Find: Height of the AB
Next solve: Angel C = 30 degrees. BC = 8mTo Find: Height of the AB
A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of 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.
From figure: Total height of the tree = AB+ACIn right ΔABC,Using Cosine and tangent angles,cos 30° = BC/ACWe know that, cos 30° = √3/2√3/2 = 8/ACAC = 16/√3 …(1)Also, tan 30° = AB/BC1/√3 = AB/8AB = 8/√3 ….(2)From (1) and (2),Total height of the tree = AB + AC = 16/√3 + 8/√3 = 24/√3 = 8√3 m.

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