17. In Fig. 10.49, PS = 3 cm, Qs = 4 cm, <PRQ = (theta) , <PSQ = 90°,PQ is perpendicular to RQ and
RQ = 9 cm. Evaluate tan theta.
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Step-by-step explanation:
ANSWER
In figure ST || QR
and PS= 3 cm & RS= 4cm
In ΔPST & PQR
QPR=∠TPS [Common]
∠PRQ=∠PST [corresponding]
ΔPQR∼ΔPST [AA similarity]
Now
In similar triangles ratios of the area of triangles is equal to the ratio of the square of corresponding sides.
Ar. ofΔPRQ
Ar.ofΔPST
(
3+4
3
)
2
=
49
9
Hence [
Ar.ofΔPRQ
Ar.ofΔPST
=
49
9
]
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