In the figure, ABC is a right-angled triangle in which
angle ABC = 90° and AB = 4 cm. BD is perpendicular to AC and angle ABD = ø, where tan ø = 0.5. Find the length of AC
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From the figure, we have
cos45
∘
=
AC
AB
⇒AC=
cos45
∘
AB
=
1
2
4
=4
2
cm
Now, sin45
∘
=
AC
BC
⇒BC=AC×sin45
∘
=4
2
×
2
1
=4 cm
Also, sin45
∘
=
AB
BD
⇒BD=AB×sin45
∘
=4×
2
1
=2
2
cm.
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