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To indirectly measure the distance across a lake, Zahra makes use of a couple landmarks at points O and P....

To indirectly measure the distance across a lake, Zahra makes use of a couple landmarks at points O and P. She measures NQ, QO, and QR as marked. Find the distance across the lake (OP), rounding your answer to the nearest hundredth of a meter.
Diagram labels: QO = 140 m, NQ = 145 m, QR = 84.8 m. Right angles are marked at O and Q.
(Diagram is not to scale.)

Answer

Triangles NQR and NOP are similar: both are right triangles and share the angle at N. Since NO = 145 + 140 = 285 m, corresponding sides give OP/84.8 = 285/145.

Therefore, OP = 84.8 × 285/145 ≈ 166.68 meters.

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