Question

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse B A is 9.8 inches, the length of C B is 6.3 inches, and the length of C A is 7.5 inches.
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)

Answer 1

Answer:

$\angle B=\cos^{-1}\left(\dfrac{6.3}{9.8}\right)\\ \\\angle B=\sin^{-1}\left(\dfrac{7.5}{9.8}\right)$

Step-by-step explanation:

Consider right triangle ABC with right angle C.

In this triangle,

• BA = 9.8 in
• CB = 6.3 in
• CA = 7.5 in

Write trigonometric functions:

$\cos \angle B=\dfrac{BC}{AB}=\dfrac{6.3}{9.8}\\ \\\sin \angle B=\dfrac{AC}{AB}=\dfrac{7.5}{9.8}$

Hence,

$\angle B=\cos^{-1}\left(\dfrac{6.3}{9.8}\right)\\ \\\angle B=\sin^{-1}\left(\dfrac{7.5}{9.8}\right)$

Answer 2

Answer:

C

Step-by-step explanation:

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