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How do you prove that two right triangles are congruent if the hypotenuse and an acute angle of one are equal respectively to the hypotenuse and acute angle of the other?
Let ABC and DEF be triangles which are right angled at A and D, such that the hypotenuses BC and EF are equal and, without loss of generality, angle B = angle E.ThenThen by the sine rule, BC/sin(A) = AC/sin(B) and EF/sin(D) = DF/sin(E)Since angle A = angle D = pi/2 radians, then sin(A) = sin(D) = 1so that BC/sin(A) = BC while EF/sin(D) = EFtherefore, since the hypotenuses BC and EF are equal, the left hand sides of the two equations are equal.Therefore, AC/sin(B) = DF/sin(E)then, since angle B = angle E, then sin(B) = sin(E) so that AC = DF.Also, angle C = pi/2 - angle Band angle F = pi/2 - angle Ethe right hand sides are equal so angle C = angle F.Then in a manner similar to the above, we can show that AB = DE.Thus all three pairs of corresponding sides are equal and all three pairs of corresponding angles are equal so that the two triangles are congruent.
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
Does the index of refraction equal the angle of refraction?
Not exactly, the angle of refraction = the angle of incidence, which means the ratio of sine of angle of incidence to the sine of angle of refraction is constant for two media. That is sin i /sin r = constant , and this constant is called refractive index
The angle at which light strikes a surface is the same as the angle at which it is reflected?
Yes. Light follows the law of signs and Sin(I)/vi = Sin(R)/vr . Because vi=vr the angles are equal. This important law in physics is often stated as follows: Angle of Reflection = Angle of Incidence
How do you calculate the angle if you know Sin of the angle?
type the value of sine in the calculator and press 2ND SIN for sin-1, or press 2ND SIN for sin-1 and type the value of sine, because -sin(.xxxx) = angle known as inverse sine
Can sin equal 2?
No. Sin of any angle is always less than or equal to 1.
At what angle measure are the sin and the cosine equal?
45 degree
How do you prove that two right triangles are congruent if the hypotenuse and an acute angle of one are equal respectively to the hypotenuse and acute angle of the other?
Let ABC and DEF be triangles which are right angled at A and D, such that the hypotenuses BC and EF are equal and, without loss of generality, angle B = angle E.ThenThen by the sine rule, BC/sin(A) = AC/sin(B) and EF/sin(D) = DF/sin(E)Since angle A = angle D = pi/2 radians, then sin(A) = sin(D) = 1so that BC/sin(A) = BC while EF/sin(D) = EFtherefore, since the hypotenuses BC and EF are equal, the left hand sides of the two equations are equal.Therefore, AC/sin(B) = DF/sin(E)then, since angle B = angle E, then sin(B) = sin(E) so that AC = DF.Also, angle C = pi/2 - angle Band angle F = pi/2 - angle Ethe right hand sides are equal so angle C = angle F.Then in a manner similar to the above, we can show that AB = DE.Thus all three pairs of corresponding sides are equal and all three pairs of corresponding angles are equal so that the two triangles are congruent.
The refractive index of water is 1.33 a ray is incident from water on air at an angle of incidence equal to 30 degree what is the angle of refraction in air?
nwater * sin 30=nair *sin(angle of refraction) 1.33*0.5=1*sin(angle of refraction) sin(angle of refractiob)=0.665 angle of refraction inair=41.6 degrees nwater * sin 30=nair *sin(angle of refraction) 1.33*0.5=1*sin(angle of refraction) sin(angle of refractiob)=0.665 angle of refraction inair=41.6 degrees
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 does sin -1.46 equal?
Assuming the angle is given in radians, it is -0.9939
How to express sin of an angle in terms of the terminal angle?
sin312 the terminal angle of 312 is equal to 48 degrees! That's all i know!
Does the index of refraction equal the angle of refraction?
Not exactly, the angle of refraction = the angle of incidence, which means the ratio of sine of angle of incidence to the sine of angle of refraction is constant for two media. That is sin i /sin r = constant , and this constant is called refractive index
The angle at which light strikes a surface is the same as the angle at which it is reflected?
Yes. Light follows the law of signs and Sin(I)/vi = Sin(R)/vr . Because vi=vr the angles are equal. This important law in physics is often stated as follows: Angle of Reflection = Angle of Incidence
Write down the acute angle whose sine is equal to Cos 70?
cos70=sin20 so angle is 20, because cosA=sin(90-A)
What does 1 - cos squared equal?
Note that an angle should always be specified - for example, 1 - cos square x. Due to the Pythagorean formula, this can be simplified as sin square x. Note that sin square x is a shortcut of (sin x) squared.
How do you calculate the angle if you know Sin of the angle?
type the value of sine in the calculator and press 2ND SIN for sin-1, or press 2ND SIN for sin-1 and type the value of sine, because -sin(.xxxx) = angle known as inverse sine
