Given the diagrams here, how do I find all the missing parts?

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1 Answer
Jim G.
Nov 22, 2017

#"see explanation"#

Explanation:

#"given angles of "45^@" and "90^@#

#"then third angle "=180-45-90=45^@#

#"hence the triangle is a right angled isosceles"#

#rArr"the legs are equal in length"#

#"the hypotenuse "=2sqrt2#

#"using "color(blue)"Pythagoras' theorem"#

#"let the length of leg "=x#

#rArrx^2+x^2=(2sqrt2)^2#

#rArr2x^2=8rArrx^2=4rArrx=2#

#rArr"legs are of length 2 units"#

#color(blue)"Second diagram"#

#"using the same method as above on the triangle on"#
#"the right"#

#x^2+x^2=(4sqrt2)^2#

#rArr2x^2=32rArrx^2=16rArrx=4#

#rArr"legs are of length 4 units"#

#"using the "color(blue) "trig ratio tan"" on the left triangle"#

#tan60^@="opposite"/"adjacent"=4/"adjacent"#

#rArr"adjacent "=4/(tan60^@)=4/sqrt3=(4sqrt3)/3larr"short leg"#

#("hypotenuse ")^2=4^2+((4sqrt3)/3)^2#

#color(white)(xxxxxxxxxx)=16+48/9=192/9#

#rArr"hypotenuse "=sqrt(192/9)=8/3sqrt3#

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