In triangle PQR, <P=90 degrees, <Q=10.5 degrees and RQ=120 cm. Find PR.
PR/QR = sin(Q)
PR/120 = sin(10.5)
Triangle
To find the length of PR in triangle PQR, we can use the trigonometric ratio sine.
In a right-angled triangle, the sine of an angle is equal to the length of the side opposite to the angle divided by the hypotenuse. In this case, PR is the hypotenuse of the right-angled triangle PQR.
Let's write the equation for the sine of angle Q:
sin(Q) = opposite / hypotenuse
sin(10.5 degrees) = PQ / PR
Now, we can rearrange the equation to solve for PR:
PR = PQ / sin(10.5 degrees)
To find PQ, we can use the trigonometric ratio tangent.
In a right-angled triangle, the tangent of an angle is equal to the length of the side opposite to the angle divided by the length of the side adjacent to the angle. In this case, PQ is the side adjacent to angle Q.
Let's write the equation for the tangent of angle Q:
tan(Q) = opposite / adjacent
tan(10.5 degrees) = RQ / PQ
Now, we can rearrange the equation to solve for PQ:
PQ = RQ / tan(10.5 degrees)
Substituting the value of RQ = 120 cm and tan(10.5 degrees) into the equation, we can calculate PQ.
PQ = 120 cm / tan(10.5 degrees)
After finding the value of PQ, we can substitute it back into the equation PR = PQ / sin(10.5 degrees) to calculate PR.