What is the area of a right triangle when the hypotenuse is 5 cm long and one angle is x/10 radians?

Question

What is the area of a right triangle when the hypotenuse is 5 cm long and one angle is  radians?

Grade 12 Advanced Functions (MHF4U)

Please write neatly and clearly. Thanks

Answer 1

Area = base×height/2

base = 5cos(θ)

height = 5sin(θ)

θ=π/10 radians = 18°

Area = 5cos(θ)5sin(θ)/2

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Or using the sine formula for the area of a triangle

Area = absin(C)/2 where C in this case is π/2, since this is a right triangle. So sine(C) = 1

a = 5sin(A)

b = 5cos(B)

A=B=π/10

Just plug in the values to get the Area.