Question 624493: The hypotenuse of a right triangle is 5 inches. if one leg is 2 inches, find the degree measure of each angle
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! hypotenuse is 5 inches.
1 leg is 2 inches.
from the pythagorean formulla, a^s + b^2 = c^2 here a and b are legs and c is the hypotenuse.
you get:
2^2 + b^2 = 5^2 which simplifies to":
4 + b^2 = 25
solve for b^2 to get:
b^2 = 25 - 4 = 21
b equals sqrt(21)
your triangle has legs of 2 and sqrt(21) and a hypotenuse of 5 where:
a = 2
b = sqrt(21)
c = 5
angle A is opposite side a
angle B is opposite side b
angle C is opposite side c
angle C is equal to 90 degrees.
now you use the trigonometric formulas for sine, cosine, and tangent to get:
sin(A) = opp/hyp = 2/5
sin(B) = opp/hyp = sqrt(21)/5
you can use your calculator to find A and B.
C is equal to 90 degrees.
A is equal to sin^-1(2/5) which is equal to 23.57817848 degrees.
B is equal to sin^-1(sqrt(21)/5) which is equal to 66.42182152
23.57817848 + 66.42182152 = 90 degrees as they should since the sum of the angles of a triangle = 180 degrees and 90 + 90 (angle C) is equal to 180.
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