The plot map is drawn to a scale of 1:500. On the map, the distance between two boundary markers is 166 mm. Determine the actual distance between the boundary markers.

Provide the answer to an accuracy of 1 meter.

A side of the triangle is 1500 mm. A line parallel to this side divides another side into segments with lengths of 400 mm and 710 mm. The 400 mm segment is closer to the initially mentioned 1500 mm side.

Determine the length of the segment of the triangle inside the intersecting line.

Provide the answer to an accuracy of 1 mm.

Below is the side view of a uniformly tapering wedge. The wedge narrows uniformly towards its right end.

The thickness at the left end is 20.0 mm, and at the right end, it is 10.0 mm. The length of the wedge is 150.0 mm.

What is the thickness of the wedge at a point 60.0 mm from its narrow end?

Provide the result to an accuracy of 0.1 mm.

The height of the triangle is 9.0 cm. The triangle is intersected by a line parallel to the base, at a distance of 3.0 cm from the base. In what ratio does the line divide the other two sides of the triangle?

Since this is a numerical question for Moodle, only a numerical answer is acceptable. Provide the answer by calculating the numerical value of the ratio. Give the answer such that the numerator is the length of the segments on the side closer to the apex, and the denominator is the length of the segments on the side closer to the base.

Provide the answer with one decimal place.

To determine the height of a flagpole standing on a level lawn, a measuring stick 1.80 m long was placed next to it, and the lengths of the shadows of the flagpole and the measuring stick were measured. The length of the measuring stick's shadow was found to be 2.50 m, and the length of the flagpole's shadow was 12.00 m.

Determine the height of the flagpole to an accuracy of 0.01 m.  

From the vectors and we know that , and . Determine the angle between   :n and  

in degrees to one decimal place.

What is the angle between vectors and ?

Give the answer to one decimal place in degrees.

Calculate the dot product of the vectors   = [0, 3, 4] ja  = [-8, 7, -2].

Give the answer as a real number to two decimal places.

Determine such that the vectors and are perpendicular to each other.

Give the value of to two decimal places.

What is the area of the parallelogram determined by the vectors = [-4.3; 4.8; -1.4] ja  = [0.8; -3.2; -4.8] ?

Give the answer as a real number to two decimal places.