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Question

the base and altitude of a right angled triangle are 12cm and 5 cm resp.the perpendicular distance of its hypotenuse from the opposite vertex is?

Answer 1

Let the triangle be ABC, with angle B as the right angle.
BC=base=12 cm
AB=height=5 cm
By using Pythagoras Theorem, we get the hypotenuse AC to be 13 cm.
From B, draw BD perpendicular to AC.
Triangle ABC is similar to triangle BDC.
AC/BC=AB/BD
13/12=5/BD
BD=12*5/13
=4.615 cm (approx.)

Answer 2

The perpendicular distance from hypotenuse to opposite vertex is 4.61cms.

5^2 + 12^2 = 169 = 13^2
Hypotenuse is 13cms

Consider right angled triangle ABC, with Angle A = 90 degrees.

AB= 5 cms (altitude)
AC = 12 cms (base)
BC= 13cms hypotenuse

From point A, draw a perpendicular to BC. The line joining BC at point O.

We have to measeure distance AO, assume y cms.

Assume BO = x cms and OC = (13 - x) cms
From triangle AOC, AO^2 + OC^2 = AC^2
i.e., y^2 + (13-x)^2 = 144 ....... 1

From triangle AOB, AO^2 + OB^2 = AB^2
i.e., y^2 + x^2 = 25 .......2

Evaluating equations 1 and 2, we get x = 1.92 cms and y = 4.61 cms.



Another method is:

Let Angle C be called as ALPHA

From Triangle AOC,
sin(ALPHA) = OA/AC = y/12 ..... a

But from Triangle ABC, sin(ALPHA) = 5/13.....b

Equating a and b, we get y = 4.61 cms;

This is the shortest method!!!


I hope this answers your question!!!

Answer 3

Let the triangle be ABC, with angle B as the right angle.
base BC=12 cm
height AB=5 cm
By using Pythagoras Theorem, we get the hypotenuse AC equal to 13 cm.
From B, draw BO perpendicular to AC.
Triangle ABC is similar to triangle BOC.
AC/BC = AB/BO
13/12 = 5/BO
BO = 12 × 5/13
= 4.6154 cm

Answer 4

12^2 = 144 and 5^2 = 24 so 144+25= 169 so hypotenuse = 13 which is found by 169^(1/2)

for other types of right triangles with sides a and b and h for the hypotenuse: h^2 = a^2+ b^2

in case you don't know ^2 is a symbol for squared, although you probably assumed that

Answer 5

you have to use the pythagurous theorum formulae which says c^2=a^+b^.so c becomes your hypotenuse,a and b can be any of the other sides of the triangle.
so: c^2=12^2+5^2
c^2=144+25
c^2=169
than now we only want the c not the ^2 with it so we will use opposite operation,so opposit of ^2 is square root.

root of c^2=root of 169
c=13cm (dont forget the unit)

Answer 6

You can find this answer by Pythagoras Theroram that is:-
Hypotenuse square = Perpendicular square + Base square
So,
(H)sq.=(5)sq. + (12)sq.
(H)sq.=25cm + 144 cm
(H)sq.=169cm
(H)sq.=(13)sq.
(H) =13cm
So, the base of triangle = 12cm.
the Perpendicular of triangle = 5cm.
the Hypotenuse of triangle = 13cm.

Answer 7

Since this is a right triangle and we know the length of its two legs, we then know that:

5^2 + 12^2 = h^2. (h = length of hypotenuse)
25 + 144 = h^2.
169 = h^2.
h = 13.

Answer 8

Draw Δ ABC right angle at B
Hypotenuse = AC
AB = 5 cm
BC = 12 cm
tan C = 5 / 12
C = 22.6°
Let required distance = d
sin C = d / 12
d = 12 sin Ø
d = 4.62 cm

Answer 9

you are required to find the value of hypotenuse.

a^2 + b^2 = c^2
12^2 + 5^2 = c^2

c^2 = 144 + 25
c^2 = 169

c = 13 cm

Answer 10

hyp=sq rt{(12)^2+5^2}=sq rt(144+25)=sq rt(169)=13
let us assume per.from B falls at o,on hypo.
& divides it into x & 13-x,so we have
OB^2=5^2-x^2---------------(1)
&OB^2=12^2-(13-x)^2-------(2)
from (1) & (2),we get
5^2-x^2=12^2-(13-x)^2
or25-x^2=144-(169+x^2-26x)
or 25-x^2=144-169-x^2+26x
or -x^2+x^2-26x=144-169-25
or -26x=-50
or x=50/26=1.92 cm
Now from (1)we have
OB^2=5^2-x^2=25-(1.92)^2
OB^2 =25-3.69=21.31
so OB=sq rt(21.31)=4.61 cm(app)ans