EXERCISE 17 B
Question 1
Two sides begin , calculate the third side marked by letter in each right angled triangle:
Sol :
Question 2
Calculate the length of the ramp
Sol :
Question 3
Calculate the length of the wire
Sol :
Question 4
Look at the figure at the right. If you walk at the speed of 8 m/sec , how much longer will take you to walk from A to B and then from B to C, then directly from A to C ?
Sol :
Question 5
When the sun is directly overhead , a 4 m rod is held in an inclined position so that its shadow is 3 m long . how much higher is one end of the rod than the other ?
Sol :
Question 6
A tree is broken by the wind as shown n the figure . If the point from where it broke is 5 m above the ground and its top touches the ground at a distance of 12 m from its foot , find the total height of the tree before it broke.
[Hint: CD =AC]
Sol :
Question 7
Two chimneys 18 m and 13 m high stand upright in a ground . If their feet are 12 m apart , then find the distance between their tops.
[Hint: find AD]
Sol :
Question 8
Determine if a triangle with sides of the given lengths is a right triangle. if the triangle is not right angled say whether it is acute angled or obtuse angled.
(i) 15,20,25
(ii) 10,24,26
(iii) 21,28,35
(iv) 12.6,3.2,13
(v) 4.5,11.7,12.5
(vi) 55,48,73
Sol :
Question 9
(i) Calculate the lengths of
(a) AB
Sol :
In ΔADB, Using Pythagoras theorem
$Hypotenuse^2=Height^2+Base^2$
$AB^2=BD^2+AD^2$
$AB^2={36}^2+{27}^2$
$AB=\sqrt{1296+729}$
$AB=\sqrt{2025}$
AB=45
(b) BC
Sol :
In ΔCDB, Using Pythagoras theorem
$Hypotenuse^2=Height^2+Base^2$
$BC^2=BD^2+DC^2$
$BC^2={36}^2+{48}^2$
$BC=\sqrt{1296+2304}$
$BC=\sqrt{3600}$
BC=60
(ii) Prove the triangle ABC is right angled
Sol :
In ΔABC, Using Pythagoras theorem
$Hypotenuse^2=Height^2+Base^2$
$AC^2=BC^2+AB^2$
${AD+DC}^2=60^2+45^2$
${AD+DC}^2=3600+2025$
${27+48}^2=3600+2025$
${75}^2=5625$
5625=5625
ΔABC satisfies Pythagoras theorem therefore it is a right angled triangle
Question 10
The following problems relate to an isosceles triangle. Recall that if AD is drawn perpendicular to BC, then BD = DC.
Calculate the lengths marked with letters in figures (i)-(iv)
Sol :
Question 11
Given that √3=1.732 , find the altitude of an equilateral triangle whose one side measures 6 cm .
Sol :
No comments:
Post a Comment