In a triangle PQR if PQ=PR and ∠QPR=30° Then find the measure of ∠PQR.
full explanations please
Answers
Answer:
Solution
Correct option is
B
The area of the triangle PQR is 25
3
and ∠QRP=120
o
C
The radius of the incircle of the triangle PQR is 10
3
−15
D
The area of the circumcircle of the triangle PQR is 100π
(A) cos30
o
=
2×10
3
×10
(10
3
)
2
+(10)
2
−(PR)
2
⇒
2
3
=
200
3
400−(PR)
2
⇒PR=10
∵QR=PR ⇒PQR=∠QPR
∠QPR =30
o
(B) Area of △PQR =
2
1
×10
3
×10×sin30
o
=
2
1
×10×10
3
×
2
1
=25
3
∠QRP=180
o
−(30
o
+30
o
)=120
o
(C) r=
S
△
=
(
2
10+10+10
3
)
25
3
=
10+5
3
25
3
=5
3
⋅(2−
3
)=10
3
−15
(D) R=
2sinA
a
=
2sin30
o
10
=10
∴ Area =πR
2
=100π
Step-by-step explanation:
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Given:
In a triangle PQR if PQ=PR and ∠QPR=30°
Solution:
Know that angles opposite to the equal sides of a triangle are also equal.
Refer the figure given below,
Since,
In ,
Put, and
Hence, the measure of angle PQR is .