You are standing at a certain distance from a building that is 20 meters tall. the angle of elevation that the top of the building makes with your feet is 45°. if you walk 6 meters toward the building, the angle of elevation changes to blank°.

55 degrees

Step-by-step explanation:

In the initial position, the angle of elevation of the 20 meter building to your feet is 45 degrees, that means that you are at 20 meters from the building (thus forming an isosceles triangle with with the building, with internal angles 456  degrees, 90 degrees, and 45 degrees.

When you walk 6 meters towards the building, you are now at 14 meters from it. Therefore you need to examine now another triangle where the angle is unknown but for which you know the opposite side (20 meters of the building's height), and the adjacent side (14 meters of your distance to the building). See image attached for more clarity on the picture you need to study.

The tangent of this new angle is defined as opposite side divided by adjacent (opp/adj) which in our case renders 20/14 = 10/7

So to find the angle, we need to apply the arctangent function to this value.

Therefore:

new angle = arctan(10/7) = 55 degrees

large crystals result from very slow cooling.

evaporation of water: this would produce an evaporite which is a sedimentary rock. like a salt pan in a desert. not possible to have volcanic rocks originate this way.

crystalization in molten earth: slow cooling over time. (hundreds to millions of years)

crystalization at earth's surface: this results in fast cooling. (a few hours to a few months or years)

crystalization from cooling off hot water: that would be a hydrothermal deposit. while associated with volcanics they are not volcanic rocks themselves and usually occur fairly rapidly.