Trigonometry

When you have a triangle that is not a right triangle, and let's say you are using the Law of Cosines to determine an angle measure, what side do you use in place of c in the Pythagorean Theorem portion of the Law? For example, if you have a triangle with 13, 10, and 9 (and not a right triangle to distinctly have a hypotenuse measure) do you use the longest side for the formula? Hoping this makes sense. The question I'm working on is multiple choice, and every option is an answer depending on the way you solve with which numbers. Thanks.

1. 👍 0
2. 👎 0
3. 👁 118
1. You can label it any old way.
a^2 = b^2+c^2 - 2 b c cos A
the trick is to use the cosine of the angle opposite the side you are solving for.
If a = 13, b = 10, c = 9 then
a^2 = b^2 + c^2 - 2 bc cos A
b^2 = a^2 + c^2 - 2 ac cos B
c^2 = a^2 + b^2 - 2 ab cos C

Te last one is the one you see in your text, but any angle in the triangle can be C as long as you solve for the side opposite that angle.

1. 👍 1
2. 👎 0

I usually find the angle opposite the largest side, just in case that angle is obtuse. Your calculator will give you that obtuse angle using the inverse cosine function.
In most cases, once you find one of the angles using the cosine law, one of the other angles can be found using the sine law, and then the third angle can be found using the 180° sum principle.
However, if you find a small angle using the cosine law, you could run into the ambiguous case, one of the other angles could be either obtuse acute (the sine is positive in quads I and II), but your calculator would give you only the acute angle.
e.g. Suppose in triangle ABC, a=8, b=4 and c = 5
Finding angle B:
4^2 = 5^2 + 8^2 - 2(5)(8)cosB
cosB = (25+64-16)/80
B = 24.1°
Now using the Sine Law:
sinA/8 = sin24.1/4
sinA = 8sin24.1/4 = .8166...
A = 54.9°, which then makes C = 101° , but clearly A must be the largest angle since it is opposite the largest side.

The explanation is that from
sinA = 8sin24.1/4 = .8166...
A could be 54.9° or 180-54.° which would be 125.2° , the correct answer.

Finding the largest angle using the Cosine Law avoids that ambiguous case.

1. 👍 0
2. 👎 0

Similar Questions

1. math plz check ;-;

A triangle has sides of lengths 5 cm, 5 cm, and square root 47cm. Which of the following statements is true? A. The triangle is an obtuse triangle because (√47)^2>5^2+5^2 B. The triangle is an acute triangle because 5^2

asked by leo on May 31, 2016
2. math plz check ;-; sorry

A triangle has sides of lengths 5 cm, 5 cm, and square root 47cm. Which of the following statements is true? A. The triangle is an obtuse triangle because (√47)^2>5^2+5^2 B. The triangle is an acute triangle because 5^2

asked by leo on May 31, 2016
3. math

This question is suppose to be simple but i keep getting it wrong Triangle LMN has vertices L(1, 6), M(6, 3) and N(5, 7). What type of triangle is Triangle LMN? Select all that apply Scalene triangle Right triangle Isosceles

asked by Jakis on March 1, 2017
4. math plz help ;-;

A triangle has sides of lengths 5 cm, 5 cm, and square root 47cm. Which of the following statements is true? A. The triangle is an obtuse triangle because (√47)^2>5^2+5^2 B. The triangle is an acute triangle because 5^2

asked by leo on June 1, 2016
5. Math

Triangle ABC has angles measuring 137°, 15°, and 28°. Classify the triangle by its angle measures. right triangle acute triangle obtuse triangle multiangular triangle I thinks it's c

asked by Connexus Girl on December 20, 2017
1. Math

A triangle has 2 angles that measure 60 each. Which of the following best describes thiz triangle. A. Right isoseles triangle B. Equilateral triangle C. Obtuse isosceles triangle D. Acute scalene triangle

asked by Help on March 2, 2011
2. Math

Classify the triangle by its sides. Triangle has side lengths of 15, 15, and 20. Scalene Triangle. Isosceles Triangle. Equilateral Triangle. Right Triangle.

asked by idk on May 14, 2019
3. Math HELP

#1 find the value of x if RS = 4(x-3)+6 and RT = 5(2x-6). x= 12 x= 6 x= 4*** x= 3 #2 which of the following statements are always true? Choose all that apply. If the circumcenter of a triangle lies on the triangle, then the

asked by Tony on October 16, 2018
4. Math

Triangle L'M'N' is a dilation of triangle LMN. If the scale factor of the dilation is 1/5, which of the following statements is true? Triangle L'M'N' is a rotation of triangle LMN. Triangle L'M'N' is the same size as triangle LMN.

asked by Anonymous on May 8, 2014
5. math

if the measures of the angles of a triangle are represented by 2x, 3x-15, and 7x-15, the triangle is 1)an isosceles triangle 2)a right triangle 3)an acute triangle 4)an equiangular triangle

asked by derek on May 30, 2008
6. math

if the measures of the angles of a triangle are represented by 2x, 3x-15, and 7x+15, the triangle is 1)isosceles triangle 2)right triangle 3)acute triangle 4)equiangular triangle

asked by derek on May 30, 2008

More Similar Questions