Question

Triangles ABD and BCD are right-angled triangles.

A
5 cm
B
x cm
Work out the value of x.
Give your answer correct to 2 decimal places.
10 cm
D
4 cm
C

Answer 1

Solution:
In triangle ABC,
Angle ABC = 90 degrees
AD= h = 10 cm
AB= p =5cm
BD = b = ?

Now,
Tan 90= p/b
or, 1/0= 5/BD
or, BD = 0 cm

In triangle BCD,
Let,
BC = h = xcm
BD = b = 0 cm
DC = 4cm
Using the Pythagoras theorem,
h = ( p^2 + b^2)^1/2
or, x = (4^2 + 0^2)^1/2
or, x = (16 + 0)^1/2
or, x = (16)^1/2
or, x = 4 cm

Hence, The value of x is 4 cm.