Question

Four explorers are trying to find the distance across an oddly shaped lake. They position themselves as shown in the diagram. Alhombra uses her compass to instruct Chou and Duong to move along the line they form with Bizet until she sees that from her perspective the angle between Bizet and Chou is equal to the angle formed between Chou and Duong. They measure the distance between Bizet and Chou to be 35 m, between Chou and Duong to be 46 m, and between Alhombra and Duong to be 100 m. How long is the lake from east to west? Round your answer to the nearest tenth of a meter.