Advertisements
Advertisements
Question
The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is ______.
Options
25 m
13 m
18 m
17 m
Advertisements
Solution
The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is 18 m.
Explanation:
Let BC is the broken part of tree and AB is the unbroken part of tree.
Here, ΔABC is right angled triangle.
∴ (BC)2 = (AB)2 + (AC)2
⇒ (BC)2 = (5)2 + (12)2
⇒ (BC)2 = 25 + 144 = 169
⇒ (BC)2 = 132
⇒ BC = 13 m
∴ Actual height of tree is AB + BC = (5 + 13) m = 18 m.
APPEARS IN
RELATED QUESTIONS
Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 50 cm, 80 cm, 100 cm
In an equilateral triangle ABC, D is a point on side BC such that BD = `1/3BC` . Prove that 9 AD2 = 7 AB2
In the given figure, ABC is a triangle in which ∠ABC> 90° and AD ⊥ CB produced. Prove that AC2 = AB2 + BC2 + 2BC.BD.
Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)
M andN are the mid-points of the sides QR and PQ respectively of a PQR, right-angled at Q.
Prove that:
(i) PM2 + RN2 = 5 MN2
(ii) 4 PM2 = 4 PQ2 + QR2
(iii) 4 RN2 = PQ2 + 4 QR2(iv) 4 (PM2 + RN2) = 5 PR2
A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.
Find the Pythagorean triplet from among the following set of numbers.
2, 4, 5
In a square PQRS of side 5 cm, A, B, C and D are points on sides PQ, QR, RS and SP respectively such as PA = PD = RB = RC = 2 cm. Prove that ABCD is a rectangle. Also, find the area and perimeter of the rectangle.
An isosceles triangle has equal sides each 13 cm and a base 24 cm in length. Find its height
In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.
