Question

Which expressions can be used to find m∠ABC? Select two options. cos−1(StartFraction 9.8 Over 6.3 EndFraction) cos−1StartFraction 6.3 Over 9.8 EndFraction) cos−1(StartFraction 7.5 Over 9.8 EndFraction) sin−1(StartFraction 9.8 Over 7.5 EndFraction) sin−1(StartFraction 7.5 Over 9.8 EndFraction)


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Answer 1

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$cos^{-1} \frac{6.3}{9.8}$

$sin^{-1} \frac{7.5}{9.8}$

${\underline\mathrm\pink{Step-by-step\:explanation:}}$

The cosine an angle in a triangle is the length of the adjacent divided by the length of the hypotenuse.

Likewise, the sine an angle in a triangle is the length of the opposite divided by the length of the hypotenuse.

Also, in a right-angled triangle, the hypotenuse is always the longest side. This means hypotenuse is greater than both opposite and adjacent.

The value of the angle of a right-angled triangle can be derived from inverse sine or inverse cosine

Since hypotenuse is always greater than both opposite and adjacent and hypotenuse is always the denominator calculating both sine and cosine, options A $(cos^{-1}\frac{9.8}{6.3})$ and D $(sin^{-1}\frac{9.8}{7.5})$ are invalid since they have smaller denominator.

This leaves us with B, C and E. From the remaining options, it can be deduced that the is hypotenuse 9.8.

If we assume the adjacent is 7.5, this makes option C correct and from Pythagoras’ theorem, the opposite would be 6.3 and this gives an expression $sin^{-1} \frac{6.3}{9.8}$. This expression does not exist in the options. Therefore, option C is not correct.

Now if we assume the adjacent is 6.3, this makes option B correct and from Pythagoras’ theorem, the opposite would be 7.5 and this gives an expression $sin^{-1} \frac{7.5}{9.8}$. This expression is equal to option E. Therefore, options B $(cos^{-1} \frac{6.3}{9.8})$ and E $(sin^{-1} \frac{7.5}{9.8})$ are correct.

${\huge{\underline{\pink{\mathrm{Hope\:It\:Helps}}}}}$

Answer 2

Answer:

3m2n – StartFraction 2 m Over n EndFraction + StartFraction 1 Over n EndFraction StartFraction 2 m n Over 5 EndFraction – StartFraction StartRoot m EndRoot Over 4 EndFraction + 4m5 StartFraction 4 m cubed Over

Step-by-step explanation: