book Maths Puzzle Numerical Ability

If a 17-ft. ladder is leaning against a building. The base of the ladder is 7 feet from the base of the building. How high up the side of the building is the top of the ladder?

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How do you find eigenvectors? Can find eigenvalues but coming up with the vectors after the system has been solved, is eluding me. Need step by step instruction. If log8 (little 8)M= log5 (little 5)7/log5(little 5)8, then M = ?