Question

Area: Geometry Assessed here: Problem solving, concepts & procedure.

The qesution: Katta and Dalle are out with their sailboat. They sail towards a bridge and wonder if the boat with the mast goes under the bridge. They start doing some calculations to see if it goes under the bridge. The distance from the foot of the mast and straight out towards the stern is 4.5 metres. From the mast to the sternbrace, it is 0.8 meters higher up and parallel to the first measurement. That distance is 4.20 meters. See figure and determine the height of the mast.

Answer 1

To determine the height of the mast, set up a proportion using the concept of similar triangles and solve for 'h'. The height of the mast is approximately 0.857 meters.

Step-by-step explanation:

To determine the height of the mast, we can use the concept of similar triangles. The distance from the foot of the mast to the stern is 4.5 meters, and from the mast to the sternbrace, it is 0.8 meters higher up and parallel to the first measurement, which is 4.20 meters. Let's call the height of the mast 'h'.

We can set up a proportion using the similar triangles:

4.5 / h = 4.2 / 0.8

Cross-multiply to solve for 'h':

4.5 * 0.8 = 4.2 * h

3.6 = 4.2h

Divide both sides by 4.2:

3.6 / 4.2 = h

h ≈ 0.857 meters

Therefore, the height of the mast is approximately 0.857 meters.