Question

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

Answer 1

Answer:

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

$\cos 28\° = \dfrac{17}{c}$

Step-by-step explanation:

Given:

Let label the figure first such that

In Δ ABC , ∠C = 90° , ∠ B = 62°,

$\sin 62\°=\dfrac{17}{c}$

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

$\cos A = \dfrac{\textrm{side adjacent to angle A}}{Hypotenuse}$

Substituting the values we get

$\cos 28\° = \dfrac{AC}{AB}=\dfrac{17}{c}\\\\\cos 28\°=\dfrac{17}{c}$

Here in this figure

$\tan B = \dfrac{\textrm{side opposite to angle B}}{\textrm{side adjacent to angle B}}$

$\sin A = \dfrac{\textrm{side opposite to angle A}}{Hypotenuse}$

Substituting we get

$\tan 62\° = \dfrac{17}{BC}$

$\cos 62\° = \dfrac{BC}{c}$

$\sin 28\° = \dfrac{BC}{c}$

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

$\cos 28\° = \dfrac{17}{c}$