An equilateral triangle (one with all sides the same length) has an altitude of 16.8 inches. Find the length of the sides. (Round your answer to one decimal place.)

19.4 inches

Step-by-step explanation:

We are asked to calculate the length of the sides of an equilateral triangle, given the altitude.

Let the length of the side of the triangle be x Inches

We can visualize the equilateral triangle as two different right angled triangles which are joined together. Each of the right angled triangle has an hypotenuse x inches, opposite, which is the altitude of length 16.8 inches and the base of length x/2 or 0.5x

Now we can solve for x using trigonometric ratio.

Sin 60 = 16.8/x

x = 16.8/sin60

x = 19.4 inches

19.4 inch

Step-by-step explanation:

Since it is an equilateral triangle, all the sides and angles are equal.

Each of the angle of an equilateral triangle =60°

Using trigonometry, In Right angle triangle ABC

Sin 60 = 16.8/Hypotenuse

AB X Sin60= 16.8

AB= 16.8/Sin60° =19.4 inch

Each of the sides of the equilateral triangle is 19.4 inch (correct to 1 decimal place)

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