Question

Solve for X. Round your answer to the nearest tenth.

Answer 1

Basically add up the given side lengths and subtract that from 180 for the triangles

Answer 2

Based on the right-angled triangles shown above, the values of x are;

1. x = 15.9

2. x = 17.5

3. x = 7.3

4. x = 12

In Mathematics and Geometry, Pythagorean's theorem is an Euclidean postulate that can be modeled or represented by the following mathematical equation:

`c^2=a^2+b^2`

Where:

• a is the opposite side of a right-angled triangle.
• b is the adjacent side of a right-angled triangle.
• c is the hypotenuse of a right-angled triangle.

Part 1.

By applying Pythagorean's theorem, the right-angled triangle can be modeled by this equation;

`x^(2) =17^2-6^2\\\\x^(2) =289-36\\\\x=√(253)`

x = 15.9

Part 2.

By applying Pythagorean's theorem, the right-angled triangle can be modeled by this equation;

`x^(2) =15^2 +9^2\\\\x^(2) =225+81\\\\x=√(306)`

x = 17.5

Part 3.

By applying Pythagorean's theorem, the right-angled triangle can be modeled by this equation;

`x^(2) =11.2^2-8.5^2\\\\x^(2) =125.44-72.25\\\\x=√(53.19)`

x = 7.3

Part 4.

Since triangle DEF is an equilateral triangle, it is composed of a 30-60-90 right-angled trangle;

x = hypotenuse/2

x = 24/2

x = 12