The signs are ambiguous

Geometry Level 2

I've drawn a triangle which has two sides of length 1 and one $60^\circ$ angle not in between these two sides.

When I measure the remaining side and find its length to be also 1, I conclude the triangle is equilateral.

Now, suppose that the $60^\circ$ above is replaced with some other acute angle and this time I have no way of measuring the remaining side.

Which of the following could be the resultant figure?

Select one or more

Acute triangle Obtuse triangle

1 solution

Blan Morrison
Oct 22, 2018

Since the triangle has 2 equal side lengths, we know it is an isosceles triangle. Therefore, the replaced angle $(\theta)$ is the same as the angle on the bottom left of the triangle. Knowing this, the top angle can be represented by the expression $180-2\theta$ . Therefore, we can use inequalities to see if the triangle can be obtuse and/or acute is $\theta <90$ : $180-2\theta >90$ $-2\theta >-90$ $\theta<45$ This means that the triangle will be an obtuse triangle is the angle is less than 45. Likewise, the triangle will be acute if the angle is greater than 45. Therefore, we can have both types of triangles. $~\beta_{\lceil \mid \rceil}$

The signs are ambiguous

1 solution

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