Now that we have a basic understanding of what the trig functions sine, cosine, and tangent represent, and we can use our calculators to find values of trig functions, we can use all of this to solve some word problems. In this reading we'll simply look at examples of word problems, and then let you give them a try.

Sample #1
The sun's angle of inclination is 20 degrees, and a pole casts a 40 foot shadow. How tall is the pole?
 

Solution
Using the image above, X = 20 degrees, and y = 40 ft.

tan X = x / y
0.3640 = x / 40
x = 14.56 ft

Sample #2
A ramp is 50 feet long, and it is set at a 30 degree angle of inclination. If you walk up the ramp, how high off the ground will you be?

Solution
Using the image above, X = 30 degrees and z = 50 ft.

sin X = x / z
0.5 = x / 50
x = 25

Sample #3
A man walks 5 miles at 60 degrees north of east. How far east of his starting point is he?

Solution
Using the image above, with y representing the eastern travel, x representing the northern travel, and z representing the actual path of the man,

sin X = x / z
0.8660 = x / 5
x=4.33 miles.

 

1.

A man travels at 30 degrees north of east, and ends up 10 miles east of his starting point. How far did he travel?

2.

A flag pole is 20 feet tall. If the sun's angle of inclination is 50 degrees, how long is the pole's shadow?

3.

A mountain has a 20 degree slope, and is 1 mile tall. How far do you need to hike to reach the summit?

4.

A building casts a 70 foot shadow when the sun's angle of inclination is 40 degrees. How tall is the building?

5.

A man travels at 10 degrees north of west, and ends up 5 miles north of his starting point. How far west of his starting point will he end up? (HINT: You'll need to draw a triangle that's oriented differently from the one in the reading!)

6.

A mountain has a 35 degree slope, and you must hike 7 miles to reach the summit. How tall is the mountain?

7.

An airplane is 2000 feet above the ground. The sun's angle of inclination is 40 degrees. How far is the airplane's shadow from the point on the ground directly under the airplane?

8.

An ant is standing as far away from a flagpole as it can while still standing in the shadow of the pole. The pole is 25 feet tall, and the sun's angle of inclination is 30 degrees. What is the distance from ant to the top of the pole?

9.

Jill walks 10 miles at 40 degrees south of west. How far west of her starting point does she end up?

10.

Jack walks 30 miles at 30 degrees north of east, then walks 30 miles at 45 degrees north of east. How many miles east of his starting point will he end up?