Kayla W. Sin X= 0.7547 sin A= 0.4540 cos Y= 0.5736 cos B= 0.5000 tan B= 0.6239 tan C= 0.1405 2 Answers By Expert Tutors
X=48.99916333 degrees, use a trig calculator that has inverse functions. That definitely rounds to 49 for nearest degree. Another way to view X is sin45 is a common angle whose sine is sq2/2 = 0.707. .7547 is slightly more than .707, so X is slightly more than 45 degrees. 49 looks about right. sinA = .4540, A=27.00061091 degrees or 27 rounded off. Use a calculator with an inverse sine function. Also .454 is close to .5. .5 = 1/2 which is the
sin30, a common angle in trig. .454 is slightly less than .5, so A is slightly less than 30. 27 looks about right. cosY= .736 Y=42.60821753 = 43 degrees rounded off. Again, .736 is a little over .707 = sqr2/2, a common right triangle with 45 degrees. 43 is slightly less than 45, and .736 is slightly more than .707 If you drew a picture, a graph, it would make sense. cosB = 0.5 = 1/2. B = 60 degrees. It's that common right triangle with angles 30-60-90 that you'll see popping up a lot in trigonometry. Almost as common as the 45-45-90 degree right triangle. tanB=0.6239 B=31.96 = 32 degrees 32 is close to 30. tan30 = 1/sqr3 = 0.577 32 is a little more than 30, so tan32 is a little more than tan30. .6239 is a little more than .577 tanC =.1405. C=7.9977 = 8 degrees any tangent less than 1 is less than 45 degrees. .1405 is about 1/7 of 1. 1/7 of 45 is about 6 1/2 degrees. 8 degrees is in the right range for the solution. But use a calculator to get the more precise answer Also each of these answers at a minimum include +n360 where n= any integer. some have another answer as well. sinX >0 could be in quadrant I or II. a reference angle of 49 degrees in quadrant II is 131 degrees. then add +n360 to that where n= any integer. There's an infinite number of solutions to each of these problems.
 Still looking for help? Get the right answer, fast.ORFind an Online Tutor Now Choose an expert and meet online. No packages or subscriptions, pay only for the time you need. This Calculation Equation & Triangle\( A = \sin^{-1} \left[ \dfrac{a \sin B}{b} \right]\)
A = angle A B = angle B C = angle C a = side a b = side b c = side c P = perimeter s = semi-perimeter K = area r = radius of inscribed circle R = radius of circumscribed circle *Length units are for your reference-only since the value of the resulting lengths will always be the same no matter what the units are. Calculator UseUses the law of sines to calculate unknown angles or sides of a triangle. In order to calculate the unknown values you must enter 3 known values. Some calculation choices are redundant but are included anyway for exact letter designations. Calculation MethodsTo calculate any angle, A, B or C, say B, enter the opposite side b then another angle-side pair such as A and a or C and c. The performed calculations follow the side side angle (SSA) method and only use the law of sines to complete calculations for other unknowns. To calculate any side, a, b or c, say b, enter the opposite angle B and then another angle-side pair such as A and a or C and c. The performed calculations follow the angle angle side (AAS) method and only use the law of sines to complete calculations for other unknowns. Law of SinesIf a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of sines states: \( \dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C} \) Equations from Law of Sines solving for angles A, B, and C\( A = \sin^{-1} \left[ \dfrac{a \sin B}{b} \right] \) \( A = \sin^{-1} \left[ \dfrac{a \sin C}{c} \right] \) \( B = \sin^{-1} \left[ \dfrac{b \sin A}{a} \right] \) \( B = \sin^{-1} \left[ \dfrac{b \sin C}{c} \right] \) \( C = \sin^{-1} \left[ \dfrac{c \sin A}{a} \right] \) \( C = \sin^{-1} \left[ \dfrac{c \sin B}{b} \right] \) Equations from Law of Sines solving for sides a, b, and c\( a = \dfrac{b \sin A}{\sin B} \) \( a = \dfrac{c \sin A}{\sin C} \) \( b = \dfrac{a \sin B}{\sin A} \) \( b = \dfrac{c \sin B}{\sin C} \) \( c = \dfrac{a \sin C}{\sin A} \) \( c = \dfrac{b \sin C}{\sin B} \) Triangle CharacteristicsTriangle perimeter, P = a + b + c Triangle semi-perimeter, s = 0.5 * (a + b + c) Triangle area, K = √[ s*(s-a)*(s-b)*(s-c)] Radius of inscribed circle in the triangle, r = √[ (s-a)*(s-b)*(s-c) / s ] Radius of circumscribed circle around triangle, R = (abc) / (4K) References/ Further ReadingWeisstein, Eric W. "Law of Sines" From MathWorld-- A Wolfram Web Resource. Law of Sines. Zwillinger, Daniel (Editor-in-Chief). CRC Standard Mathematical Tables and Formulae, 31st Edition New York, NY: CRC Press, p. 512, 2003. http://hyperphysics.phy-astr.gsu.edu/hbase/lcos.html http://hyperphysics.phy-astr.gsu.edu/hbase/lsin.html |
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