Find the missing angle.

Mathematics

1 answer:

Wittaler [7]3 years ago

5 0

The triangle to the top right is missing one angle. We know the sum of all angles in a triangle add up to 180 degrees. We already have 35 + 90 = 125 degrees, so the last angle must be 55 degrees. That angle is verticle to another angle, which you should be able to notice (also 55 degrees because vertical angles are congruent). Now, we have 67 + 55 = 122 degrees in that triangle. It must add up to 180, so the unknown angle is 58 degrees.

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△ABC is a right triangle with right angle C. Side AC is 6 units longer than side BC . If the hypotenuse has length 52–√ units,

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Step-by-step explanation:

A right triangle has two legs and a hypotenuse. The hypotenuse is opposite the right angle. As Angle C is the right angle, then the triangle can be constructed as shown in the picture attached. The sides of the triangle have a relationship known as the Pythagorean Theorem a² + b² = c². In the theorem, the legs of the triangle are a and b while the hypotenuse is c. Substitute a = x, b = x+6, and c = √52. Simplify and solve.

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x² + (x+6)² = √52²

x² + x² + 12x + 36 = 52

2x² + 12x - 16 = 0

You can use the quadratic formula to solve by substituting a = 2, b = 12, and c = -16.

The quadratic formula is $x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$ .