in triangle pqr angle pqr is 90° QS is perpendicular to PR and ST is perpendicular to QR if PQ is equal to 6 cm and PS is equal to 3 cm find area of the triangle QST by area of the triangle RST
Answers
Answered by
11
Final Answer : 1/3
Steps and Understanding :
1) In PQS,
cos (P) = PS/PQ
=> cos(P) = 3/6 = 1/2
=> P = 60°
2) Now, finding other angles as shown in pic by using properties of triangle.
3) In PQS,
tan(60°) = QS/PS
=> QS = 3* tan(60°) = 3√3cm
In QST,
sin(60°) = ST/QS
=> ST =( 3√3) * (√3/2 )
=> ST = 9/2 cm.
cos(60°) = QT/QS
=> 1/2 = QT/QS
=> QT = 3√3 * (1/2)
=> QT = 3√3/2 cm
4) In RST,
tan(30°) = ST/TR
=> 1/√3 = (9/2)/ TR
=> TR = 9√3/2 cm.
5) Now, Finally
area ( QST) / area (RST) =
( 1/2 * QT* ST )/( 1/2 * RT* ST)
=QT/RT
=
Hence, Required Ratio is 1/3 .
Steps and Understanding :
1) In PQS,
cos (P) = PS/PQ
=> cos(P) = 3/6 = 1/2
=> P = 60°
2) Now, finding other angles as shown in pic by using properties of triangle.
3) In PQS,
tan(60°) = QS/PS
=> QS = 3* tan(60°) = 3√3cm
In QST,
sin(60°) = ST/QS
=> ST =( 3√3) * (√3/2 )
=> ST = 9/2 cm.
cos(60°) = QT/QS
=> 1/2 = QT/QS
=> QT = 3√3 * (1/2)
=> QT = 3√3/2 cm
4) In RST,
tan(30°) = ST/TR
=> 1/√3 = (9/2)/ TR
=> TR = 9√3/2 cm.
5) Now, Finally
area ( QST) / area (RST) =
( 1/2 * QT* ST )/( 1/2 * RT* ST)
=QT/RT
=
Hence, Required Ratio is 1/3 .
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Answered by
11
Answer:
Step-by-step explanation:
Final Answer : 1/3
Steps and Understanding :
1) In PQS,
cos (P) = PS/PQ
=> cos(P) = 3/6 = 1/2
=> P = 60°
2) Now, finding other angles as shown in pic by using properties of triangle.
3) In PQS,
tan(60°) = QS/PS
=> QS = 3* tan(60°) = 3√3cm
In QST,
sin(60°) = ST/QS
=> ST =( 3√3) * (√3/2 )
=> ST = 9/2 cm.
cos(60°) = QT/QS
=> 1/2 = QT/QS
=> QT = 3√3 * (1/2)
=> QT = 3√3/2 cm
4) In RST,
tan(30°) = ST/TR
=> 1/√3 = (9/2)/ TR
=> TR = 9√3/2 cm.
5) Now, Finally
area ( QST) / area (RST) =
( 1/2 * QT* ST )/( 1/2 * RT* ST)
=QT/RT
=
Hence, Required Ratio is 1/3 .
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