Question

A road sign is in the shape of an equilateral triangle with a vertical measurement of 41.2cm. How long is each side?

Answer 1

Okay this seems hard, and the replies online are extremely complicated but I'll do my best. explaining in simple terms. :)

As you know, all triangles have 180 degrees, so in an equilateral triangle each angle is 60 degrees.

Then you split the triangle in half, forming 2 smaller triangles that have a right angle.

In the new smaller triangle, you have to find x, which is the hypotenuse along with being a side of the real triangle.

As you know previously, 1 angle is 90 degrees, and theta is equal to 60 degrees. Also 41.2 is the height along the shared side in the real triangle.

Now, the trigonometry ratio to use is Sine. As you know, sin = opposite/hypotenuse. So from the perspective of theta, 60 degrees, the opposite side is 41.2 and the hypotenuse is x.

From here on, if x is in the denominator you flip the equal around, take for example:
original equation:
sin(60) = 41.2/x
turning x into the subject (on the numerator line) equation:
x = 41.2/sin(60)

To put short, it is simply x and sin(60) replacing each other, to make x the subject.

Then you use your calculator, and the answer is 47.57cm

Hopefully this was helpful :)