In △PQR, the measure of angle Q is 90
∘
. If tanP=
3
4
and 1.5cm, then what is the length (in cm) of side PR?
- A2
- B2.5
- C3
- D4.8
Solution & Step-by-step Explanation
In right-angled △PQR:
tanP=
Adjacent
Opposite
=
PQ
QR
=
3
4
Let QR=4x and PQ=3x.
Given that PQ=1.5cm:
3x=1.5⟹x=0.5
So, the side QR is:
QR=4x=4×0.5=2cm
By Pythagoras' theorem, the hypotenuse PR is:
PR=
PQ
2
+QR
2
=
(1.5)
2
+2
2
=
2.25+4
=
6.25
=2.5cm
tanP=
Adjacent
Opposite
=
PQ
QR
=
3
4
Let QR=4x and PQ=3x.
Given that PQ=1.5cm:
3x=1.5⟹x=0.5
So, the side QR is:
QR=4x=4×0.5=2cm
By Pythagoras' theorem, the hypotenuse PR is:
PR=
PQ
2
+QR
2
=
(1.5)
2
+2
2
=
2.25+4
=
6.25
=2.5cm