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In right triangle XYZ, ∠Z is a right angle, m∠Y=16∘, and XZ=7. sin16∘≈0.276 cos16∘≈0.961 tan16∘≈0.287. What is the measurement of YZ?

In right triangle XYZ Z is a right angle mY16 and XZ7 sin160276 cos160961 tan160287 What is the measurement of YZ class=

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bridgetstem

Answer: 24.4

Step-by-step explanation:

So lets review a bit about sine, cosine, and tangent.

Look at attachment below

Okay so we have the opposite side of the triangle and are trying to find the length of the adjacent side. The only trig expression that contains both opposite and adjacent is tangent. The equation goes

tanX = opposite(XZ)/adjacent (YZ)

we know what X is X = 16

and we know what opposite is opposite = 7

so now the equation looks like

tan16 = 7/adjacent

and in the question it says that tan16 = 0.287 so lets plug that in

0.287 = 7/adjacent

0.287adjacent = 7

adjacent = 7/0.287

adjacent = 24.4

YZ = 24.4

Ver imagen bridgetstem

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