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# Use the Pythagorean theorem to find x

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The triangle is an isosceles triangle. The height is 6 with the altitude bisecting the base. The base is x while the sides of the triangle are unknown. The angles of the triangle on the base are both 60 degrees. I am supposed to use the Pythagorean theorem to find x the base of the triangle.

Jan 11, 2021

#1
+11231
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Use the Pythagorean theorem to find x.

The triangle is an isosceles triangle. The height is 6 with the altitude bisecting the base. The base is x while the sides of the triangle are unknown. The angles of the triangle on the base are both 60 degrees. I am supposed to use the Pythagorean theorem to find x the base of the triangle.

Hello Guest!

$$Kosinus =\frac{Ankathete}{Hypotenuse}$$

$$cos(60^{\circ})=0.5=\large \frac{\frac{x}{2}}{s}\\ 0.5s= \frac{x}{2}$$

$$s=x$$

The Pythagorean theorem:

$$\color{blue}s^2=6^2+(\frac{x}{2})^2\\ s=x\\ x^2=36+\frac{x^2}{4}\\ x^2-\frac{x^2}{4}=36$$

$$\frac{3x^2}{4}=36\\ x^2=\frac{4\cdot 36}{3}=48\\ x^2=3\cdot 4^2$$

$$x=4\cdot \sqrt{3}\\ x=6.928$$

!

Jan 11, 2021
edited by asinus  Jan 11, 2021
#2
+1162
+1

The triangle is an isosceles triangle. The height is 6 with the altitude bisecting the base. The base is x while the sides of the triangle are unknown. The angles of the triangle on the base are both 60 degrees. I am supposed to use the Pythagorean theorem to find x the base of the triangle.

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h = 6         ∠θ = 60º        x = ?

(x / 2)2 = (h / sin∠θ)2 - h2

x = 6.92820323  or   x = 4√3

Jan 11, 2021
edited by jugoslav  Jan 11, 2021
edited by jugoslav  Jan 11, 2021