Answer:
1.7 in.
Step-by-step explanation:
Draw an equilateral triangle with a horizontal side on the bottom. All sides are congruent, and all angles are congruent. Each side measures 2 inches. Each angle measures 60 degrees.
Now draw the altitude from the top vertex to the bottom horizontal side. The altitude is perpendicular to the horizontal side and bisects it. Now you have two right triangles inside the original equilateral triangle. The hypotenuse of each right triangle is a side of the original equilateral triangle. It measures 2 in. Since the bottom 2-inch side of the original equilateral triangle was bisected by the altitude, the short leg of each right triangle is half the length of the side of the equilateral triangle. Therefore, the short leg of each right triangle measures 1 inch. We can find the length of the long leg (the altitude of the equilateral triangle) by using the Pythagorean theorem. Let the unknown height be h.
[tex] 1^2 + h^2 = 2^2 [/tex]
[tex] 1 + h^2 = 4 [/tex]
[tex] h^2 = 3 [/tex]
[tex] h = \sqrt{3} [/tex]
Take the square root of 3. You'll get 1.73205...
Round it off to the nearest tenth to get 1.7.
Answer: 1.7 in.
