# law of sines answer key

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[/latex]Find side$\,a$ when$\,A=132°,C=23°,b=10. Suppose two radar stations located 20 miles apart each detect an aircraft between them. If there is more than one possible solution, show both. At the corner, a park is being built in the shape of a triangle. \frac{ sin( \red b)}{ 16} = \frac{ sin(115)} {123} \\ To do so, we need to start with at least three of these values, including at least one of the sides. Solving for[latex]\,\gamma ,$ we haveWe can then use these measurements to solve the other triangle. Round your answers to … \\ Since we do In which triangle(s) below, can we use the formula? $$\frac{ \red b}{ sin(118)} = \frac{ 11 } {sin(29)} The first search team is 0.5 miles from the second search team, and both teams are at an altitude of 1 mile. Round each answer to the nearest tenth. Real World Math Horror Stories from Real encounters In this case, we know the angle$\,\gamma =85°,\,$and its corresponding side$\,c=12,\,$and we know side$\,b=9.\,$We will use this proportion to solve for$\,\beta . (Follow up from question 3). If the man and woman are 20 feet apart, how far is the street light from the tip of the shadow of each person? \frac{ \red e}{ sin(67)} = \frac{ 7 } {sin(54)} Use the fact the sum of the interior angles of a triangle is 180° to calculate all of the angles inside the What is the distance from[latex]\,A\,$to$\,B,\,$rounded to the nearest whole meter?A man and a woman standing$\,3\frac{1}{2}\,$miles apart spot a hot air balloon at the same time. (They would be exactlythe same if we used perfect accuracy). [/latex]The aircraft is at an altitude of approximately 3.9 miles.Access these online resources for additional instruction and practice with trigonometric applications.The altitude extends from any vertex to the opposite side or to the line containing the opposite side at a 90° angle.When can you use the Law of Sines to find a missing angle?When the known values are the side opposite the missing angle and another side and its opposite angle.In the Law of Sines, what is the relationship between the angle in the numerator and the side in the denominator?What type of triangle results in an ambiguous case?A triangle with two given sides and a non-included angle.For the following exercises, assume$\,\alpha \,$is opposite side$\,a,\beta \,$is opposite side$\,b,\,$and$\,\gamma \,$is opposite side$\,c.\,$Solve each triangle, if possible. Instead, we can use the fact that the ratio of the measurement of one of the angles to the length of its opposite side will be equal to the other two ratios of angle measure to opposite side. Law Of Sines And Cosine.$$ Point$\,C\,$is 97 meters from$\,A.\,$The measure of angle$\,BAC\,$is determined to be 101°, and the measure of angle$\,ACB\,$is determined to be 53°. The Law of Sines Name_____ Date_____ Period____-1-State the number of possible triangles that can be formed using the given measurements.

1) m A 31°, c mi, a mi 2) m B 82°, a m, b m 3) m B 110°, b m, a ) m4 m A 64°, c in, a in Find each measurement indicated.

\frac{ \red e}{ sin(67)} = \frac{ 7 } {sin(54)} In some cases, more than one triangle may satisfy the given criteria, which we describe as an ambiguous case.
\\ Solving an oblique triangle means finding the measurements of all three angles and all three sides.

We found some Images about Trigonometry The Law Of Sines Worksheet Answer Key: The satellite is approximately 1706 miles above the ground.A communications tower is located at the top of a steep hill, as shown in The roof of a house is at a$\,20°\,$angle.



One side of the proportion has side A and the sine of its opposite angle .

\frac { \color{red}{x} }{ sin(116)} = \frac{19}{sin (34) }

Round each answer to the nearest tenth.Find angle$A$when[latex]\,a=24,b=5,B=22°.