Concept explainers
a.
To calculate: The measure of
a.
Answer to Problem 21PSD
The measure of angle R is
Explanation of Solution
Given information:
In
Side PQ = 10,
Side PR = 12.
∠ Q =
Formula used:
Calculation:
In ΔPQR,
b.
To find: The side QR if side angle Q is
b.
Answer to Problem 21PSD
The side QR is
Explanation of Solution
Given information:
In triangle PQR ,
Side PQ = 10,
Side PR = 12.
∠ Q =
Formula used:
The below theorem is used:
Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
In right angle triangle,
Calculation:
In ΔPQR,
Side PQ = 10.
Side QS can be calculated by applying Pythagoras Theorem.
In right angled triangle PSQ , we get
Side PR = 12.
Side SR can be calculated by applying Pythagoras Theorem.
In right angled triangle PSR , we get
c.
To show: The ratio of side PR to sine of angle Q is equal to ratio of side PQ to sine of angle R .
c.
Explanation of Solution
Given information:
In triangle PQR ,
Side PQ = 10,
Side PR = 12.
∠ Q =
Formula used:
The below theorem is used:
Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
In right angle triangle,
Proof:
In ΔPQR,
Side PQ = 10.
Side QS can be calculated by applying Pythagoras Theorem.
In right angled triangle PSQ , we get
Side PR = 12.
Side SR can be calculated by applying Pythagoras Theorem.
In right angled triangle PSR , we get
From Equation 1 and Equation 2, we get
d.
To show: The ratio of side PR to sine of angle Q is equal to ratio of side PQ to sine of angle R if triangle PQR is acute triangle.
d.
Explanation of Solution
Given information:
In triangle PQR ,
Side PQ = 10,
Side PR = 12.
∠ Q =
Formula used:
Proof:
In ΔPQS,
In ΔPRS,
From Equation 1 and Equation 2, we get
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