Lucy has to run two errands. She starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. Then, from the gas station, she travels 5 miles to return home. The entire trip forms a triangle. What was the smallest angle made in her trip?

Smallest angle =

Step-by-step explanation:

Given that:

Let the home be at the point A.

Lucy travels 3 miles south to reach point B.

Then 4 miles to east to reach point C and then

returns to home traveling 5 miles making it a triangle for the whole journey.

This travel is nothing but forms a right angled , right angled at point B.

To find:

Smallest angle in the travel.

Solution:

In a triangle, the smallest angle is the angle opposite to the smallest side.

Therefore, the will be the smallest.

We can use tangent trigonometric ratio here:

Therefore, the answer is:

Smallest angle =

step-by-step explanation:

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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