Question

In exercises 3 and 4 , find the values of x and y.

Answer 1

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:

`\tan \theta=\frac{\text{opposite side}}{adjacent\text{ side}}`

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