Question

In ∆IJK, j=7.6cm, k=7.8cm and < I=27°. Find the length of i, to the nearest 10th of a centimeter.

Answer 1

The diagram of the triangle is shown below

To find i, we would apply the cosine rule which is expressed as

a^2 = b^2 + c^2 - 2bcCosA

If we compare this rule with the given triangle, then

a = i

angle A = angle I = 27 degrees

b = 7.6

c = 7.8

Thus, we have

i^2 = 7.6^2 + 7.8^2 - 2 * 7.6 * 7.8Cos27

i^2 = 57.76 + 60.84 - 118.56Cos27

i^2 = 118.6 - 105.64

i^2 = 12.96

$\begin{gathered} i\text{ = }\sqrt[]{12.96} \\ i\text{ = 3.6} \end{gathered}$

The length of i is 3.6 centimeters