Question

Right angle triangle.A right angle triangle has a 40 degree angle and hypotenuse = 10. Find the other  angles and sides.

Accepted Answer

The angles of a triangle add up to 180. As one of the angles is 40 and it is a right triangle, the angles are 90, 40 and 50.
The hypotenuse is 10.
If the side opposite 40 degrees is S, sin 40  = S / 10
=> S = 6.427
Similarly the side opposite 50 degrees is 7.66
The angle and the side opposite them are 40, 6.427; 50, 7.66; 90, 10

Answer

If the angle A is of 90 degrees, then  B+C = 40 + C = 90
C = 90 - 40
C = 50 and B = 40
We'll apply the Pythagorean theorem and the sine function.
sin B = x/10
sin 40 = x/10
x = 10*sin 40
x = 10*0.64
x = 6.4 units
We'll apply Pythagorean theorem in a right angle triangle:
10^2 = x^2 + y^2
100 = 40.96 + y^2
y^2 = 100 - 40.96
y^2 = 59.04
y = 7.6 units
We'll keep only the positive value for y, since a length cannot be negative.

Math

Right angle triangle.A right angle triangle has a 40 degree angle and hypotenuse = 10. Find the other angles and sides.

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