$$Real World Math Horror Stories from Real encounters Showing top 8 worksheets in the category - Law Of Sines And Cosine. A 6-foot-tall man is standing on the street a short distance from the pole, casting a shadow. One side of the proportion has side A and the sine of its opposite angle . We found some Images about Trigonometry The Law Of Sines Worksheet Answer Key: [/latex]To find the remaining missing values, we calculate$\,\alpha =180°-85°-48.3°\approx 46.7°.\,$Now, only side$\,a\,$is needed. Solving for$\,\gamma ,$ we haveWe can then use these measurements to solve the other triangle. nearest tenth. Suppose two radar stations located 20 miles apart each detect an aircraft between them. The inverse sine will produce a single result, but keep in mind that there may be two values for$\,\beta .\,$It is important to verify the result, as there may be two viable solutions, only one solution (the usual case), or no solutions.In this case, if we subtract$\,\beta \,$from 180°, we find that there may be a second possible solution. 14.6 m 20. Round the distance to the nearest tenth of a foot.Three cities,$\,A,B,$and$\,C,$are located so that city$\,A\,$is due east of city$\,B.\,$If city$\,C\,$is located 35° west of north from city$\,B\,$and is 100 miles from city$\,A\,$and 70 miles from city$\,B,$how far is city$\,A\,$from city$\,B?\,$Round the distance to the nearest tenth of a mile.Two streets meet at an 80° angle. What is the area of the sign?Naomi bought a modern dining table whose top is in the shape of a triangle.$$ (Follow up from question 3). $$\frac{ \red b}{ sin(118)} = \frac{ 11 } {sin(29)} It would be preferable, however, to have methods that we can apply directly to non-right triangles without first having to create right triangles.Any triangle that is not a right triangle is an oblique triangle. Round your answers to the nearest tenth.$$ \frac{ \red b}{ sin(118)} = \frac{ 11 } {sin(29)} Round to the nearest tenth of a mile.A street light is mounted on a pole. \\ See We can stop here without finding the value of$\,\alpha .\,$Because the range of the sine function is$\,\left[-1,1\right],\,$it is impossible for the sine value to be 1.915. They then move 300 feet closer to the building and find the angle of elevation to be 50°. Find the area of the table top if two of the sides measure 4 feet and 4.5 feet, and the smaller angles measure 32° and 42°, as shown in $h=b\mathrm{sin}\,\alpha \text{ and }h=a\mathrm{sin}\,\beta$$\begin{array}{ll}\text{ }b\mathrm{sin}\,\alpha =a\mathrm{sin}\,\beta \hfill & \hfill \\ \text{ }\left(\frac{1}{ab}\right)\left(b\mathrm{sin}\,\alpha \right)=\left(a\mathrm{sin}\,\beta \right)\left(\frac{1}{ab}\right)\begin{array}{cccc}& & & \end{array}\hfill & \text{Multiply both sides by}\,\frac{1}{ab}.$To find$\,\beta ,\,$apply the inverse sine function. 105 m .

Round each answer to the nearest tenth. [/latex]Find side$\,a$ when$\,A=132°,C=23°,b=10. In this case, we know the angle[latex]\,\gamma =85°,\,$and its corresponding side$\,c=12,\,$and we know side$\,b=9.\,$We will use this proportion to solve for$\,\beta .$For the following exercises, assume$\,\alpha \,$is opposite side$\,a,\beta \,$is opposite side$\,b,\,$and$\,\gamma \,$is opposite side$\,c.\,$Determine whether there is no triangle, one triangle, or two triangles. (They would be exactlythe same if we used perfect accuracy). 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.