Question

Question #b03a6

Answer 1

`27^o` To nearest degree.

Explanation:

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.)