Question

A right triangle is shown. The hypotenuse has length b. The angle opposite to side a is y and the angle opposite to side c is x. Which equations for the measures of the unknown angles x and y are correct? Check all that apply. x = cos–1(StartFraction a Over c EndFraction) x = sin–1(StartFraction c Over b EndFraction) x = tan–1(StartFraction c Over a EndFraction) y = sin–1(StartFraction a Over c EndFraction) y = cos–1(StartFraction c Over b EndFraction)

Answer 1

Answer:

Therefore,

The correct options are

$\sin x = \dfrac{c}{b}\\\\x=sin^{-1}(\dfrac{c}{b})$

$\tan x = \dfrac{c}{a}\\\\x=tan^{-1}(\dfrac{c}{a})$

$\cos y = \dfrac{c}{b}\\\\x=cos^{-1}(\dfrac{c}{b})$

Step-by-step explanation:

Consider a right angle Triangle ΔABC, such that

AB = c = Adjacent side opposite to angle x

BC = a = Adjacent side opposite to angle y

AC = b = Hypotenuse

To Check :

For correct option?

Solution:

In Right Angle Triangle ABC,

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

$\cos x = \dfrac{\textrm{Adjacent side to angle x}}{Hypotenuse}$

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

Substituting the values we get

$\sin x = \dfrac{c}{b}\\\\x=sin^{-1}(\dfrac{c}{b})$

$\cos x = \dfrac{a}{b}\\\\x=cos^{-1}(\dfrac{a}{b})$

$\tan x = \dfrac{c}{a}\\\\x=tan^{-1}(\dfrac{c}{a})$

Now for y

$\sin y = \dfrac{a}{b}\\\\x=sin^{-1}(\dfrac{a}{b})$

$\cos y = \dfrac{c}{b}\\\\x=cos^{-1}(\dfrac{c}{b})$

Therefore,

The correct options are

$\sin x = \dfrac{c}{b}\\\\x=sin^{-1}(\dfrac{c}{b})$

$\tan x = \dfrac{c}{a}\\\\x=tan^{-1}(\dfrac{c}{a})$

$\cos y = \dfrac{c}{b}\\\\x=cos^{-1}(\dfrac{c}{b})$

Answer 2

Answer: B,D ad E

Step-by-step explanation: