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Trig: Laws of Cosines.
In Δ EFG , side e =9, side g =18 and m < F= 45* . Find side ' f' to the nearest integer.

13.3

Step-by-step explanation:

f² = e² + g² - 2(e)(g)cos(F)

f² = 9² + 18² - 2(9)(18)cos(45)

f² = 175.8974029

f = 13.262631982

Step-by-step explanation:

we would apply the law of Cosines which is expressed as

a² = b² + c² - 2abCosA

Where a,b and c are the length of each side of the triangle and A is the angle corresponding to a. Likening the expression to the given triangle, it becomes

f² = e² + g² - 2(e × g)CosF

f² = 9² + 18² - 2(9 × 18)Cos45

f² = 81 + 324 - 2(162)Cos45

f² = 405 - 324 × 0.707

f² = 405 - 229.068

f² = 175.932

f = √175.932

f = 13 to the nearest integer

f

step-by-step explanation:

f