Each diagram below shows a right triangle with the altitude drawn to the hypotenuse. How do I find the value of x, y and z?
1 Answer
Explanation:
#color(blue)"diagram on left"#
#"within the diagram there are 3 right triangles"#
#"using "color(blue)"Pythagoras' theorem"#
#color(blue)"small triangle on left"#
#y^2=x^2+4to(1)#
#color(blue)"larger triangle on right"#
#z^2=x^2+64to(2)#
#color(blue)"outer main triangle"#
#y^2+z^2=100to(3)#
#"substitute equation "(1)" into equation "(3)#
#x^2+4+z^2=100#
#"substitute equation "(2)" into this equation"#
#x^2+4+x^2+64=100larrcolor(red)"equation in one variable"#
#rArr2x^2=32rArrx^2=16rArrx=4#
#"substitute this value into equation "(1)#
#y^2=16+4rArry^2=20rArry=2sqrt5#
#"substitute x = 4 into equation "(2)#
#z^2=16+64rArrz^2=80rArrz=4sqrt5#
#"the diagram on the right is done in a similar way"#
#"you may wish to attempt it yourself for the practice"#