Now that you understand inverse trig functions, this opens up a whole new set of problems you can solve. In the previous set of problems, you were given one side length and one angle. From this you could determine other information about the triangle.

However, in real world situations you won't always know these specific pieces of information; instead you might know two side lengths. Here are some examples:

Sample #1
A 10 foot pole casts a 30 foot shadow. What is the angle of inclination of the sun?
 

Solution
Using the image above,
tan^-1 (x/y) = X
tan^-1 (10/30) = 18.43 degrees

Sample #2
A man walks in a northeasterly direction for 30 miles, and he ends up 5 miles east of his starting point. In what direction was he walking?

Solution
Using the image above,
cos^-1 (y/z) = X
cos^-1 (5/30) = 80.4 degrees North of East

Sample #3
After walking for awhile, Jack ends up twice as far east of his starting point as he is north of his starting point. In what direction was he walking?

Solution
His east distance is 2n, and his north distance is n. 

tan^-1 (n/2n) = tan^-1 (1/2) = 26.57 degrees
 

1.

After running, Maggie is 3 miles east of her starting point, and 4 miles north of her starting point. In what direction was she running?

2.

A building which is 30 feet tall casts a 5 foot shadow. What is the sun's angle of inclination?

3.

Someone hiking a straight line up a mountain trail hikes a total of 7 miles to gain 2 miles of elevation. What is the angle of inclination of the mountain trail?

4.

If Richard walks for awhile in a straight line, he ends up x miles west of his starting point, and 2x miles in a straight line from his starting point. In what direction was he walking?

5.

A 20 foot ladder is leaned against a wall, with the top of the ladder at a height of 15 feet. What is the angle of inclination of the ladder?

6.

A 30 foot ladder is leaned against a wall, and the base of the ladder is 2 feet from the base of the wall. What is the angle of inclination of the ladder?

7.

If a car travels 30 miles west and then 25 miles south, what direction is its ending point from its starting point?

8.

If a car travels 60 miles in a northwesterly direction, and ends up 30 miles west of its starting point, in what direction was the car traveling?