Answer:
The measure of <A is 67.38°.
The expression used to find the measure of angle A is sin^-1 12/13.
Step-by-step explanation:
Let's review some of the trigonometric ratios.
sin A = opp/hyp
cos A = adj/hyp
tan A = opp/hyp
opp = length of opposite leg
adj = length of adjacent leg
hyp = length of hypotenuse
Look at angle A.
The adjacent leg to angle A is AB with length 5.
The opposite leg to angle A is BC with length 12.
The hypotenuse is AC with length 13.
Using the trig ratios above, we have:
sin A = 12/13
cos A = 5/13
tan A = 12/5
Since we know the sine, cosine, and tangent of angle A, to find angle A, we use the inverse functions of the sine, cosine, and tangent, respectively.
m<A = sin^-1 12/13
m<A = cos^-1 5/13
m<A = tan^-1 12/5
Using any of the three expressions above, we get m<A = 67.38°.
Of the given choices, we choose the expression that matches one of our expressions above.
Answer:
The measure of <A is 67.38°.
The expression used to find the measure of angle A is m<A = sin^-1 12/13.
