Find the lengths of the missing sides in the triangle. Use the Triangle Theorem. Write your answers as integers, in radical form, or as decimals rounded to the nearest tenth. The diagram is not drawn to scale.
Since the triangle is a right triangle, we can use the Pythagorean theorem to find the lengths of the missing sides.
Let x be the length of the side opposite the angle labeled 40 degrees.
Using the Pythagorean theorem:
x^2 + 8^2 = 10^2
x^2 + 64 = 100
x^2 = 36
x = √36
x = 6
So, the length of the side opposite the angle labeled 40 degrees is 6 units.
Next, let y be the length of the hypotenuse.
Using the Pythagorean theorem:
6^2 + y^2 = 10^2
36 + y^2 = 100
y^2 = 64
y = √64
y = 8
So, the length of the hypotenuse is 8 units.