The outer square is 5cm by 5 cm. How do I work out the height of the triangle (the line the arrow is pointing to)?
+15001 The outer square is 5cm by 5 cm. How do I work out the height of the triangle (the line the arrow is pointing to)?
Hello Guest!
The sides of the triangle are a and b. Then
\(a+b=5\\ b=5-a\\ a^2+b^2=3.8^2\\ a^2+(5-a)^2=3.8^2\\ a^2+25-10a+a^2-3.8^2=0\)
\(2a^2-10a+10.56=0\\ a^2-5a+5.28=0\)
\(a=2.5\pm \sqrt{6.25-5.28}\\ a=2.5\pm 0.985\)
\(a=3.485\\ b=1.515\)
\(tan\ \beta=\frac{b}{a}\\ \beta=atan\ \frac{b}{a}\\ sin\ \beta=\frac{h}{a}\\ h=a\cdot sin(atan\frac{b}{a})\)
\(h=3.485\cdot sin(atan\frac{1.515}{3.485})\)
\(\large h=1.389\ cm\)
!
