Trigonometry and Triangles
To solve the problem, we need to recall the following:
* The sum of the interior angles in a triangle is 180°
* The sum of two supplementary angles is 180°
* The tangent of an acute angle in a right triangle is defined as:
[tex]\tan \theta=\frac{\text{opposite side}}{adjacent\text{ side}}[/tex]
We included a new variable z to help solve the problem. Details below:
Angle 59° and angle z° are supplementary because they are a linear pair, thus:
z + 59 = 180
Solving for z:
z = 121
Now we focus on the left triangle with interior angles of 45°, z°, and x°. The sum of all three must be 180°, thus:
45 + 121 + x = 180
Solving for x:
x = 180 - 45 - 121
x = 14
Now focus on the bigger triangle (the one that contains two smaller triangles).
This triangle is right (it has one interior angle of 90°) and it's also an isosceles triangle because it also has one interior angle of 45°.
Any right triangle
