These two law of sines problems below will show you how to use the law of sines to solve some real life problems.
Problem #1
Two fire-lookout stations are 15 miles apart, with station A directly east of station B. Both stations spot a fire. The angular direction of the fire from station B is N52°E and the angular direction of the fire from station A is N36°W. How far is the fire from station A?
Solution
The biggest trick is this problem is to understand the meaning of N52°E and N36°W.
N52°E means 52 degrees east of north.
N36°W means 36 degrees west of north.
Here is what the graph will look like.
Notice that to find 38°, you need to subtract 52° from 90°. By the same token, to find 54°, you need to subtract 36° from 90°.
Notice also that the angle opposite 15 is missing, so we need to find it.
38 + 54 + missing angle = 180
92 + missing angle = 180, so missing angle = 88
Now, we can use the law of sines to find the distance the fire is from station A.
Let x be the distance from the fire to station A.
Problem #2
The leaning tower of pisa is inclined 5.5 degrees from the vertical. At a distance of 100 meters from the wall of the tower, the angle of elevation to the top is 30.5 degrees. Use the law of sines to estimate the height of the leaning tower?
Solution
The trickiest thing here is making the graph. We show it below. Notice that the height is shown with a green line.
Let us find angle y and angle z
angle y + 5.5 = 90, so angle y = 84.5
84.5 + 30.5 + angle z =180
115 + angle z = 180
angle z = 65
Now, we can use law of sines.
Nov 09, 18 09:40 AM
Learn the three properties of congruence. Examples to illustrate which property.
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Nov 09, 18 09:40 AM
Learn the three properties of congruence. Examples to illustrate which property.
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.