GeometryIf the hypotenuse of a right triangle is 10 units and angle B is 70 degrees determine angle A and the other sides of the triangle.
The hypotenuse of the right triangle is 10 units and the angle B = 70 degrees. Let the angle which equals 90 degree be C.
The length of the side b is sin 70 = b/ 10
=> b = 9.396 units
The angle A is 20 degrees
sin 20 = a/ 10
=> a = 3.420 units
The angles of the triangle are 20, 70 and 90 and the sides are 3.42 , 9.396 and 10 units.
We'll consider the right angle: A = 90 degrees.
The hypotenuse is opposite side to the right angle.
That means that B+C = 70 + C = 90
C = 90 - 70
C = 20 and B = 70
To determine the lengths of the other cathetus, we'll apply the Pythagorean theorem and the sine function.
The sine function is a ratio between the opposite cathetus and the hypothenuse. We'll note the cathetus as x and y.
sin B = x/10
sin 70 = x/10
x = 10*sin 70
x = 10*0.93
x = 9.4 units
We'll apply Pythagorean theorem in a right angle triangle:
10^2 = x^2 + y^2
100 = 88.36 + y^2
y^2 = 100 - 88.36
y^2 = 11.64
y = 3.4 units
We'll consider only the positive value for y, since it is the length of the cathetus of the right angle triangle and it cannot be negative.