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# geometry

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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)?

Oct 1, 2020

#1
+10336
+1

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

$$a+b=5\\ b=5-a\\ a^2+b^2=3.8^2\\ a^2+(5-a)^2=3.8^2\\ a^2+25-10a+a^2-3.8^2=0$$

$$2a^2-10a+10.56=0\\ a^2-5a+5.28=0$$

$$a=2.5\pm \sqrt{6.25-5.28}\\ a=2.5\pm 0.985$$

$$a=3.485\\ b=1.515$$

$$tan\ \beta=\frac{b}{a}\\ \beta=atan\ \frac{b}{a}\\ sin\ \beta=\frac{h}{a}\\ h=a\cdot sin(atan\frac{b}{a})$$

$$h=3.485\cdot sin(atan\frac{1.515}{3.485})$$

$$\large h=1.389\ cm$$

!

Oct 1, 2020
edited by asinus  Oct 1, 2020
#2
+246
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The area of the outer square is  52 = 25 cm2

The area of the blue square is    3.82 = 14.44 cm2

The area of a triangle is   (25 - 14.44) / 4 = 2.64 cm2

The height (h) of a triangle       h = (2 * 2.64) / 3.8

h = 1.389473684 cm

Oct 1, 2020