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Chapter 7: Problem 56

Describe a strategy for solving an SSS triangle.

Short Answer

Expert verified
The strategy to solve an SSS triangle is to first use the law of cosines to find one angle, then use the law of sines or cosines to find the second angle, and finally use the fact that the sum of angles in a triangle is 180 to find the third angle.

Step by step solution

01

Find the first angle

To find the first angle (let's call it A), use the law of cosines. The law of cosines is expressed as: \( a^2 = b^2 + c^2 - 2bc \cdot \cos(A) \) where \( a, b, c \) are the sides of the triangle. Since we know all the sides we can rearrange the formula to solve for \(\cos(A)\) and then use the inverse cosine to find angle A.
02

Find the second angle

After finding angle A, now we turn our attention to finding the second angle (let's call it B). We could use the law of cosines again, but using the law of sines is generally easier. The law of sines is expressed as: \( \frac{a}{\sin(A)} = \frac{b}{\sin(B)}\). We already know a, A, and b so we can solve for sin(B) and then use the inverse sine to find angle B.
03

Find the third angle

Since we know that the sum of all angles in a triangle is 180 degrees, we can simply subtract the first two angles from 180 to get the third angle (let's call it C). So: \( C = 180 - A - B \)

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. If I know the measures of all three angles of an oblique triangle, neither the Law of sines nor the Law of Cosines can be used to find the length of a side.

A pine tree growing on a hillside makes a \(75^{\circ}\) angle with the hill. From a point 80 feet up the hill, the angle of elevation to the top of the tree is \(62^{\circ}\) and the angle of depression to the bottom is \(23^{\circ} .\) Find, to the nearest tenth of a foot, the height of the tree.

After a wind storm, you notice that your 16 -foot flagpole may be leaning, but you are not sure. From a point on the ground 15 feet from the base of the flagpole, you find that the angle of elevation to the top is \(48^{\circ} .\) Is the flagpole leaning? If so, find the acute angle, to the nearest degree, that the flagpole makes with the ground.

Convert each polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation. $$ r \cos \theta=7 $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Solving an SSS triangle, I do not have to be concerned about the ambiguous case when using the Law of sines.
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