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What is sine equation?
the sine rule, angle (a) and opposite length is eaqual to angle (b) and opposite length. which are also equal to angle (c) and opposite length. Sin A = Sin B = Sin C ------- -------- ---------- a -------- b -------- c
What is the perimeter of a triangle when an angle of 57 degrees is opposite to a side of 14.5 inches and has another angle of 71 degrees?
The sum of tthe angles of a triangle is 180° which means the third angle is 180° - (57° + 71°) = 52° The sine rule gives: a/sin A = b/sin B = c / sin C where side a is opposites angle A, etc. The sine rule can be used to find the lengths of the other two sides when the angles are all known and one side length is known. Let angle A = 57°, then side a = 14.5 in. Let angle B = 71° and angle C = 52° Using the sine rule: a/sin A = b/ sin B → b = a × sin B/sin A Similarly, c = a × sin C/sin A → The perimeter = a + b + c = a + a × sin B/sin A + a × sin C/sin A = a(1 + sin B/sin A + sin C/sin A) = 14.5 in × (1 + sin 71° / sin 57° + sin 52° / sin 57°) ≈ 44.47 in ≈ 44.5 in
How do you construct a triangle with perimeter 150 mm and a base angle 75 degrees and 30 degrees?
Perhaps you can ask the angel to shed some divine light on the question! Suppose the base is BC, with angle B = 75 degrees angle C = 30 degrees then that angle A = 180 - (75+30) = 75 degrees. Suppose the side opposite angle A is of length a mm, the side opposite angle B is b mm and the side opposite angle C is c mm. Then by the sine rule a/sin(A) = b/(sin(B) = c/sin(C) This gives b = a*sin(B)/sin(A) and c = a*sin(C)/sin(A) Therefore, perimeter = 150 mm = a+b+c = a/sin(A) + a*sin(B)/sin(A) + a*sin(C)/sin(A) so 150 = a*{1/sin(A) + sin(B)/sin(A) + sin(C)/sin(A)} or 150 = a{x} where every term for x is known. This equation can be solved for a. So draw the base of length a. At one end, draw an angle of 75 degrees, at the other one of 30 degrees and that is it!
Explain what the Law of sines becomes when one of the angles is a right angle?
The Law of sines: a/sin A = b/sin B = c/sin CIf the angle C in the triangle ABC is 90 degrees, then the triangle ABC is a right triangle, where c is the measure of the hypotenuse, a is the measure of the leg opposite the angle A, and b is the measure of the leg opposite the angle B.Let us observe what happens when sin C = sin 90 degrees = 1.c/sin C = a/sin A cross multiply;c sin A = a sin C divide by c both sides;(c sin A)/c = (a sin C)/c simplify c on the left hand side;sin A = (a sin C)/c = [(a)(1)]/c = a/csin A = (measure of leg opposite the angle A)/(measure of hypotenuse)From the Law of Cosine we know that cos A= (b^2 + c^2 - a^2)/(2bc). If we substitute a^2 + b^2 for c^2, we have:cos A = (b^2 + (a^2+ b^2) - a^2 )/(2ab)cos A = 2b^2 /2ab simplify;cos A = b/c = (measure of leg adjacent the angle A)/(measure of hypotenuse) Therefore tan A = sin A/cos A =(a/c)/(b/c) = (a/c)(c/b) = a/b = (measure of leg opposite the angle A)/(measure of leg adjacent to angle A). And cot A = cos A/sin A = (b/c)/(a/c) = (b/c)(c/a) = b/a = (measure of leg adjacent to angle A)/(measure of leg opposite the angle A).
How do you find an angle when you know one other angle and two of the sides of a triangle?
If these two sides are opposite to these angles, and you know one of the angles, you can use the Law of Sines to find the other angle. For example, in the triangle ABC the side a is opposite to the angle A, and the side b is opposite to the angle B. If you know the lengths of these sides, a and b, and you know the measure of the angle B, then sin A/a = sin B/b multiply by a to both sides; sin A = asin B Use your calculator to find the value of arcsin(value of asin b), which is the measure of the angle A. So, Press 2ND, sin, value of asin B, ).
If angle A is 60 degrees angle B is 45 degrees angle C is 75 degrees and the length of side AC is 10 units then what is the length of side AB?
This problem can be solved using the Sine Rule :a/sin A = b/sin B = c/sin C 10/sin 45 = AB/sin 75 : AB = 10sin 75 ÷ sin 45 = 13.66 units (2dp)
What is the shortest side of a triangle when its longest side is 162 cm with two known angles of 37.25 degrees and 48.4 degrees?
The third angle is found to be: third_angle = 180° - (37.25° + 48.4°) = 94.35° You can now use the sine rule: a / sin A = b / sin B with a as the shortest side and A the angle opposite it (the smallest angle), and b as the longest side and B the angle opposite it (the largest angle). →a / sin 37.25° = 162 cm / sin 94.35° → a = 162 cm × sin 37.25° / sin 94.35° ≈ 98.34 cm
What is the sin of angle B if the angles are 3 4 5?
I think you have not asked the question correctly.I guess you meant that the sides of the triangle are 3, 4 and 5. Similarly you have given no indication of which angle is opposite which side.A 3, 4, 5 triangle is a right angle triangle (5 is the hypotenuse).Thus depending where angle B is, its sine will be:If B is opposite the side of length 3, sin B = 4/5If B is opposite the side of length 4, sin B = 3/5If B is opposite the side of length 5, sin B = 5/5 = 1; alternatively ∠B = 90° and sin B = sin 90° = 1
What are the formulas for law of sines and law of cosines?
sine: sin(A) sin(B) sin(C) cosines: a2=b2+c2-2bc cos(A).........----- = ----- = ------........,,,.a .......b........ ca is side BC A is angle A sin(A) means sine of angle Apsst, theres a law of tangents too, but its so complicated that im not gonna post it hereLaw of sine -A B C------ = ------ = ------Sin(a) Sin(b) Sin(c)
What is this expression as the cosine of an angle cos30cos55 plus sin30sin55?
cos(30)cos(55)+sin(30)sin(55)=cos(30-55) = cos(-25)=cos(25) Note: cos(a)=cos(-a) for any angle 'a'. cos(a)cos(b)+sin(a)sin(b)=cos(a-b) for any 'a' and 'b'.
Solve the right triangle with A equals 52 degrees 15' and a equals 6.7808?
Angle A = 52° 15' = 52 25° therefore angle B = 90 - 52.25 = 37.75°. Using the Sine Rule : a/sin A = b/sin B. 6.7808/sin 52.25 = b/sin 37.75 : b = 6.7808 sin 37.75 ÷ sin 52.25 = 5.2503 Either using the Sine Rule or Pythagoras gives the length of the hypotenuse as 8.5758
What are all the triangle formulas?
Area = (Base x Height) / 2 For a right angle triangle Pythagoreas' Theorem states: a2 + b2 = c2 sum of angles = 180o For a non-right angle triangle: { the Sine Law states: a/Sin(A) = b/Sin(B) = c/Sin(C) for ease of explanation let abc be lengths of a non-right angle triangle. {a / Sin(angle where b meets c)} = {b / Sin(angle where c meets a)} = {c / Sin(angle where a meets b)} The Cosine Law states: (with respect to the above example) a2 = b2 + c2 - 2bc Cos(A) b2 = a2 + c2 - 2ac Cos(B) c2 = a2 + b2 - 2ab Cos(C) }
