50.2k views
4 votes
The diagonals of rectangle QRST intersect at P . Given that m∠PTS=34° and QS=10 , find RP

1 Answer

1 vote

Final answer:

In a rectangle, the diagonals are congruent. We can use trigonometry to find the length of RP.

Step-by-step explanation:

In a rectangle, the diagonals are congruent, so if RP is one of the diagonals, then RQ is also equal to RP. Since RP and RQ form a right triangle, the angles RTS and RQT are complementary, which means their sum is 90 degrees (m∠RTS + m∠RQT = 90 degrees).

We are given that m∠PTS = 34 degrees. Since angles in the same segment of a circle are congruent, m∠RQT = m∠PTS = 34 degrees. Therefore, m∠RTS = 90 - 34 = 56 degrees.

Now we can use trigonometry to find the length of RP. In triangle RQT, we can use the sine function: sin(RTS) = RP / QS. Rearranging, RP = QS * sin(RTS). Substituting the values we know, RP = 10 * sin(56 degrees) ≈ 8.13 units. Therefore, RP is approximately 8.13 units.

User Abhijay Kumar
by
8.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories