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Thepotemich [5.8K]
4 years ago
12

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)

Mathematics
2 answers:
Firlakuza [10]4 years ago
7 0

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})

s2008m [1.1K]4 years ago
3 0

Answer: B,D ad E

Step-by-step explanation:

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