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. (This is a 3 mark ques)
13.856
14.852
12.856
1.732
Answers
Answer:
13.856
Step-by-step explanation:
let the broken part of the tree be AC
it is given that
distance between foot of the tree B and point C= 8cm
so, BC=8cm
Also, broken part of the tree makes 30° angel with ground
so, angel C =30°
We need to find the height of the tree
height of tree= height of broken part of the tree - height of remaining tree
height of tree = AB+ AC
since, tree was vertical to ground
so, angel ABC =90°
if right angel triangel is ABC,
cos C = side adjacement angel to c / hypotenuse
cos c = BC/AC
cos 30° = B/AC
√3/2 =B/AC
√3/2=8/AC
AC= 8×2/√3
AC=16/√3
sin30°= AB/AC
1/2 = AB/16/√3
1/2= √3/16×BC
Ab= 16/2√3
AB =8/√3
so, height of the tree = AC+BC
16/√3+8/√3
24/√3
multiply by √3 in numerator and denominator
24/√3×√3/√3
24×√3/3
=8\√3
hence, height of the tree is 13.856