The diagram shows an isosceles triangle with two sides of 100 meters and a base of 120 meters. The question asks to find the height of the triangle.

Steps to solve for the height:

1. Identify the base and equal sides: The base is 120 meters, and the two equal sides are each 100 meters.
2. Divide the triangle: Since this is an isosceles triangle, we can drop a perpendicular from the top vertex to the base, which will split the triangle into two right triangles. The base of each of these right triangles will be half of 120 meters, which is 60 meters.
3. Use the Pythagorean theorem: For one of the right triangles, the hypotenuse is 100 meters, one leg (half of the base) is 60 meters, and we need to find the other leg (the height $h$).

Using the Pythagorean theorem: $h^2 + 60^2 = 100^2$ $h^2 + 3600 = 10000$ $h^2 = 10000 - 3600 = 6400$ $h = \sqrt{6400} = 80 \, \text{meters}$

Thus, the height of the triangle is 80 meters.

The correct answer is:

• C. 80 m

Would you like further clarification or details on this solution?

Related Questions:

1. How does the Pythagorean theorem apply to right triangles?
2. Can you find the area of this triangle using the base and height?
3. How would the height change if the base were increased by 10 meters?
4. What if the two equal sides were 120 meters each instead of 100 meters—what would the new height be?
5. How can you determine the height of an equilateral triangle using only the side length?

Tip:

When dealing with isosceles triangles, splitting them into two right triangles can often simplify finding unknown dimensions using the Pythagorean theorem.