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.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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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.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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