Question

Find the value of each variable. Round your answers to the nearest tenth. (Soh Coh Toa)

Answer 1

k = 10 tan (40) = 8.39 (to 2 decimals)

J = 10 / cos(40) = 13.05 (to 2 decimals)

Explanation:

It is SOH CAH TOA, or

Sin = Opposite / Hypotenuse

Cos = Adjacent / Hypotenuse

Tan = Opposite / Adjacent

Using SOH CAH TOA,

tan(40) = k/10, so k = 10 tan (40) = 8.39 (to 2 decimals)

cos(40) = 10 / j, so J = 10 / cos(40) = 13.05 (to 2 decimals)

Answer 2

k = 8.4, j = 13.1

Explanation:

Solve for k:

`tan(40)=(k)/(10)\\10(tan(40))=k\\8.4=k`

Solve for j:

`8.4^2+10^2=j^2\\70.56+100=j^2\\170.56=j^2\\13.1=j`