Using Pythagorean theorem, the values of x are attached below
To solve these question, we are going to use Pythagorean's theorem since we are looking for a missing side in a right angle triangle.
Pythagorean Theorem
This is used to find the missing side in a right angle triangle. The formula is given as.
[tex]x^2 = y^2 + z^2[/tex]
where;
- x = hypotenuse
- y = adjacent or opposite
- z = adjacent or opposite
Triangle 1
x = ?
y = 19
z = 16
substitute the values and solve for x
[tex]x^2 = 16^2 + 19^2\\x^2 =617\\x = \sqrt{617}\\ x = 24.84[/tex]
Triangle 2
x = 16.5
y = 9.2
z = ?
substitute the values and solve for z
[tex]16.5^2 = 9.2^2 + z^2\\z^2 = 16.5 - 9.2^2\\z^2 = 187.61\\z = \sqrt{187.61}\\ z = 13.7[/tex]
Triangle 3
x = ?
y = 33
z = 15
substitute the values and solve for x
[tex]x^2 = y^2 + z^2\\x^2 = 33^2 + 15^2\\x^2 = {1314}\\x = \sqrt{1314}\\ x = 36.25[/tex]
Triangle 4
To solve for x in this triangle, we have to find the opposite side which in the attached angle which is the hypothenuse in this angle.
x = 25
y = 16
z = ?
[tex]z^2 = 25^2 - 16^2\\z^2 = 369\\z = \sqrt{369}\\ z = 19.2[/tex]
Let's use this value and solve for x
[tex]22^2 = x^2 + 19.2^2\\x^2 = 22^2 - 19.2^2 \\x^2 = 115.36\\\\x = 10.74[/tex]
From the calculations above, the values of x are attached above.
Learn more on triangles above;
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