Find the side of an equilateral triangle if its height is 4cm.
| February 28, 2021 | education
1. Vertices of the triangle – A, B, C. Height BH = 4 cm.
2. Each of the angles of this triangle (∠А, ∠В, ∠С), according to its properties, is 60 °.
3. We calculate the length of the side AB through the sine ∠A of the right-angled triangle ABН:
The sine of ∠A is equal to the quotient of dividing the length of the height of the ВН, which is in the indicated triangle leg, to the length of the side AB (hypotenuse):
∠А = 60 °. Sine 60 ° = √3 / 2.
ВН: AB = √3 / 2.
AB = BН: √3 / 2 = 4: √3 / 2 = 4 x 2 / √3 = 8√3 / 3 cm.
Answer: The side of a triangle is 8√3 / 3 centimeters.
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