Question

Construct an isosceles triangle having base 5cm with each base angle 30°​

Answer 1

Answer:

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Step-by-step explanation:

build a rough sketch of your isosceles triangle with base = 5 cm.

label the triangle ABC with the base equal to BC.

Drop a perpendicular from A to intersect with BC.

Since the triangle is isosceles, this perpendicular will also divide the angle into 2 equal parts, and will also divide BC into 2 equal parts.

You have 2 right triangles.

Assuming the altitude intersects BC at D, the right triangles are:

ABD and ACD

the 30 degree angle will be split in 2 equal parts, each of which is 15 degrees.

the base of 5 cm will be split in 2 equal parts, each of which is 2.5 cm.

sine of 15 degrees = opposite / hypotenuse = 2.5 / x

this makes x = 2.5 / sin(15)

this makes x = 9.659258263

x is equal to one of the equal legs of your isosceles triangle.

your isosceles triangle dimensions are 2 legs of 9.659258263 and one leg of 5.

now that you have one of the sides of your triangle, you can construct your isosceles triangle given one side and the base.