Numbers involved in art

Task 1: In connection with construction, it is necessary to calculate the height of neighboring buildings to ensure good lighting. Teams want to calculate the heights of buildings, but do not have the necessary tools and decided to use their knowledge of geometry for similar triangles and proportions. They made the necessary measurements and will calculate the heights of the buildings.

Task 2: Leonardo da Vinci, the great artist, engineer, constructor, turned out to be a talented musician. He constructed a silver lyre in the shape of a horse's head. In 1482, his patron Lorenzo de 'Medici sent him to bring the lyre as a gift to the Duke of Milan, Ludovico Moreau, after which Leonardo remained in Milan for years. To move from Florence to Milan, due to weather conditions and other reasons, it is necessary to pass through Genoa and Bologna. Calculate the distance from Florence to Milan, if the distance from Florence to Bologna is 100km, from Genoa to Milan is 150 km.

Task 3:The width of the rivers along the current varies. Determine the width of the river between points B and C (in meters) if AB = 40 m , BD = 32 m и CE = 60 m .

Task 4: An inclined conveyor belt is used in a bee processing plant to transport products from level 1 to level 2. Level 2 is 3 meters high compared to level 1. The distance of 8 meters is also given as shown in the drawing. The head of the department wants to extend the conveyor belt to level 3, which is 9 m high compared to level 1. Find the distances x and y shown in the drawing.