Question

In the figure below, Sin 62 degrees - 17/c. Based on the figure, which of the following equations is also true ?

A. Cos 62 degrees = 17/c
B. Tan 62 degrees = c/17
C. Cos 28 degrees = 17/c
D. Sin 28 degrees = c/17

Answer 1

Therefore Based on the Figure only the third option i.e C. ic True

`\cos 28\° = (17)/(c)`

Explanation:

Given:

Let label the figure first such that

In Δ ABC , ∠C = 90° , ∠ B = 62°,

`\sin 62\°=(17)/(c)`

AB = Hypotenuse = c

AC = 17

To Find:

True Statements

Solution:

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

`\angle A+\angle B+\angle C=180`

Substituting the values we get

`\angle A +62+90=180\\\angle A=180-152=28\\\angle A=28\°`

In Right Angle Triangle ABC , Cosine Identity we have

`\cos A = \frac{\textrm{side adjacent to angle A}}{Hypotenuse}\\`

Substituting the values we get

`\cos 28\° = (AC)/(AB)=(17)/(c)\\\\\cos 28\°=(17)/(c)`

Here in this figure

`\tan B = \frac{\textrm{side opposite to angle B}}{\textrm{side adjacent to angle B}}`

`\sin A = \frac{\textrm{side opposite to angle A}}{Hypotenuse}\\`

Substituting we get

`\tan 62\° = (17)/(BC)`

`\cos 62\° = (BC)/(c)`

`\sin 28\° = (BC)/(c)`

Therefore Based on the Figure only the third option i.e C. is True

`\cos 28\° = (17)/(c)`