Question

The Museu Blau in Barcelona, Spain, is a natural science museum built in the shape of a triangular prism. The base of the building is an equilateral triangle 180180180 meters on each side. The height of the prism is 25\,\text{m}25m25, space, m. Find the height, hhh, of the triangular base. Round your answer to the nearest tenth.

Answer 1

155.9

Explanation:

Its correct on khan

Answer 2

155.9 meters.

Step by step answer:

Please find the attachment for explanation.

Let h be height of our equilateral triangle. We have been given that the each side of our triangle is 180 meters long. Let us drop an altitude from one vertex to the base of our triangle. Altitude will bisect base length of our triangle in two equal parts.

We can find height of an equilateral triangle by using Pythagorean theorem.

`h=\sqrt{180^(2)-90^(2)}`

`h=√(32400-8100)`

`h=√(24300)`

`h=155.88457268\approx 155.9`

Therefore, height of the triangular base is 155.9 meters.