Question

Calculate the length d. Give your answer to 3 s.f. 29° 22 mm 103° 49° 98° d​

Answer 1

By applying the law of sines, the length of side d is equal to 14.4 mm.

In Mathematics and Euclidean Geometry, the law of sines states that the sine of each angle in a geometric figure is proportional to the side length opposite (directly facing) the angle;

`(sinA)/(a) =(sinB)/(b) =(sinC)/(c)`

First of all, we would determine the length of the side opposite the 29 degrees angles;

`(sin29)/(a) =(sin103)/(22)\\\\a =(22sin29)/(sin103)`

a = 10.95 mm.

Now, we can determine the length of side d as follows;

`(sin98)/(d) =(sin49)/(10.95) \\\\d=(10.95sin98)/(sin49)`

d = 14.3677 ≈ 14.4 mm.

Complete Question;

Calculate the length d. Give your answer to 3 s.f.