Question #b03a6

1 Answer
Oct 9, 2017

#27^o# To nearest degree.

Explanation:

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Since it doesn't specify which side is the hypotenuse, the triangle will be marked in the conventional manner, with side c being the hypotenuse.

Because of the large values we will reduce the dimensions by a factor of one hundred. This will not affect the size of the relevant angles .i.e similar triangles.

#c^2 = a^2+b^2#

#-> c^2=(4.9)^2+(9.6)^2=116.17=> c=sqrt(116.17)#

Since we now know all three sides and one angle, we can use the Sine Rule:

#sinA/a=sinB/b=sinC/c#

We are looking for angle A and we know angle C. So:

#sinA/a= sinC/c=> sinA=(asinC)/c#

#-> sinA= ((4.9)sin(90))/(sqrt(116.17))=4.9/(sqrt(116.17))#

#A= arcsin((4.9)/(sqrt(116.17)))=27.04^o# ( 2.d.p.)