Question

If two angles are complementary in a right triangle, then explain how you can find the

value of x if sin 440 = cos x using 2-3 sentences. In the last sentence, give the value of x.

Answer 1

46°

Explanation:

Points of note

• two angles are complementary in a right triangle
• sin 44° = cos x°

Solving

• The first thing to understand is "complementary" means that the two angles add up to 90°
• Therefore, 44 + x = 90
• x = 46°

Answer 2

46°

Explanation:

Complementary angles

Two angles whose measures sum to 90°

In a right triangle, the angle opposite the hypotenuse is always 90°.

The interior angles of a triangle sum to 180°, therefore the other two angles are complementary angles since their sum is always 90°.

So we can label one angle as
`x` and the other as
`(90-x)`.

The side opposite angle
`x` is the side adjacent to angle
`(90-x)`.

Therefore, using trig ratios, we can say that
`\sin(x) = \cos(90-x)`

So, if
`x=44` then:

`\implies \sin(44) = \cos(90-44)=\cos(46)`