In the SSA case, if the known non-included angle is acute, you have an ambiguous situation. Inverse sine is not able to distinguish whether a second angle is, say,
In the SAS and SSS congruence situations, the Law of Sines is not useful because you do not have a known angle paired with a known opposite side. You will find out how to solve these triangles in the next lesson.
Problem 4 Using the Law of Sines to Solve a Problem
Surveying A surveyor locates points A and B at the same elevation and measures distance and angles as pictured.
Plan
How do you write an equation to solve?
Write a proportion that includes the distance you know, AB, and the distance you want, BC.
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What is BC, the distance from B to the summit?
First find
Now use the Law of Sines with
The distance from B to the summit is about 5426 ft.
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What is CD, the height of the mountain above points A and B?
In right
The summit is about 2795 ft higher than points A and B.
✓ Got It?
- A landscaper sights the top of a tree at a
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions