Question

Please help i need this urgently

Answer 1

Answer:

Angle YZX = 19.7 degrees

This is the same as saying angle Z = 19.7 degrees

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Explanation:

Since there are only three letters, and nothing else, we can refer to "angle YZX" as "angle Z" to shorten things. The middle letter is what determines the vertex of the angle.

With Z as the reference angle, side XY = 7.5 is the opposite side. It's the leg furthest from the reference angle. SIde ZY = 22.3 is the hypotenuse. The hypotenuse is always opposite the 90 degree angle.

We'll use the sine rule since it connects the opposite and hypotenuse

sin(angle) = opposite/hypotenuse

sin(Z) = XY/ZY

sin(Z) = 7.5/22.3

sin(Z) = 0.336323

Z = arcsin(0.336323)

Z = 19.653008983888

Z = 19.7

In this case, rounding to 3 sig figs means rounding to 1 decimal place (the first two digits are part of the whole number while the last digit is the decimal portion).

Make sure your calculator is in degree mode. The notation "arcsin" refers to arcsine which is the same as inverse sine. Your calculator would likely have the button $\sin^{-1}$ to indicate inverse sine.

Answer 2

Answer:

Degrees: 19.7

Radians: 0.343

Step-by-step explanation:

First, let x = angle YZX.

You can solve this using sine (which as a reminder, is opposite over hypotenuse):

sin(x) = 7.5/22.3

x = arcsin(7.5/22.3)

Now you can grab out a calculator and evaluate.

If it's in degrees: 19.7

If it's in radians: 0.343

(Remember to round to 3 significant figures like the problem said)

I hope this helped you.