The lengths of the sides of a similar triangle that has a perimeter of 45 m are 12 m , 15 m , 18 m
<h3>Further explanation</h3>
Firstly , let us learn about trigonometry in mathematics.
Suppose the ΔABC is a right triangle and ∠A is 90°.
<h3>sin ∠A = opposite / hypotenuse</h3><h3>cos ∠A = adjacent / hypotenuse</h3><h3>tan ∠A = opposite / adjacent </h3>
Let us now tackle the problem!
<em>A similar triangle has the same angle, in other words the triangle has the same shape but different sizes.</em>
<u><em>Given:</em></u>
<em>The lengths of the sides of a triangle are 8 m, 10 m, 12 m</em>
![\texttt{Perimeter of First Triangle} = 8 + 10 + 12 = 30 \texttt{ m}](https://tex.z-dn.net/?f=%5Ctexttt%7BPerimeter%20of%20First%20Triangle%7D%20%3D%208%20%2B%2010%20%2B%2012%20%3D%2030%20%5Ctexttt%7B%20m%7D)
![\texttt{Perimeter of Second Triangle : Perimeter of First Triangle = 45 : 30}](https://tex.z-dn.net/?f=%5Ctexttt%7BPerimeter%20of%20Second%20Triangle%20%3A%20Perimeter%20of%20First%20Triangle%20%3D%2045%20%3A%2030%7D)
![\texttt{Perimeter of Second Triangle : Perimeter of First Triangle = 3 : 2}](https://tex.z-dn.net/?f=%5Ctexttt%7BPerimeter%20of%20Second%20Triangle%20%3A%20Perimeter%20of%20First%20Triangle%20%3D%203%20%3A%202%7D)
<em>Therefore , the lengths of the sides of a similar triangle will be:</em>
![s_1 = \frac{3}{2} \times 8 = 12 \texttt{ m}](https://tex.z-dn.net/?f=s_1%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%5Ctimes%208%20%3D%2012%20%5Ctexttt%7B%20m%7D)
![s_2 = \frac{3}{2} \times 10 = 15 \texttt{ m}](https://tex.z-dn.net/?f=s_2%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%5Ctimes%2010%20%3D%2015%20%5Ctexttt%7B%20m%7D)
![s_3 = \frac{3}{2} \times 12 = 18 \texttt{ m}](https://tex.z-dn.net/?f=s_3%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%5Ctimes%2012%20%3D%2018%20%5Ctexttt%7B%20m%7D)
<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle