Sketch a right triangle corresponding to the trigonometric function of the acute

Question

Sketch a right triangle corresponding to the trigonometric function of the acute angle ?. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of ?.

sin(?) = 20/29

Part 1 of 4

First construct a right triangle having ? as one of the acute angles.

Consider the trigonometric functionsin(?) =

.

Recall that sin(?) =

.

Find the value of x, y and z in the right triangle that corresponds to the given trigonometric function.

20

29

unknown

Part 2 of 4

By the Pythagorean Theorem,

(hyp)2 = (opp)2 + (adj)2

y

x

)2 + (z)2

Part 3 of 4

Substitute the known values and find the value of the unknown using this equation.

(  )2 = (  )2 + (z)2

Move constant terms to one side.

(z)2 = (841) ? (  )

Simplify and find the value of z.z =

=

Therefore, the adjacent side of the triangle is  .

Explanation / Answer

Therefore, the adjacent side of the triangle is 21

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