Question

Find the size of angle XYZ.
Give your answer to 1 decimal place.
15 cm
6 cm

Answer 1

Answer:  The measure of angle XYZ is 66.4°.

Step-by-step explanation:  We are given to find the size of the angle XYZ in the right-angled triangle shown.

We see from the figure that in triangle XYZ,

m∠YXZ = 90°,  XY = 6 cm and YZ = 15 cm.

For the acute angle XYZ, XY is the base and YZ is the hypotenuse.

So, we must have

$\cos m\angle XYZ=\dfrac{base}{hypotenuse}\\\\\\\Rightarrow \cos m\angle XYZ=\dfrac{XY}{YZ}\\\\\\\Rightarrow \cos m\angle XYZ=\dfrac{6}{15}\\\\\\\Rightarrow m\angle XYZ=\cos^{-1}\dfrac{2}{5}\\\\\\\Rightarrow m\angle XYZ=\cos^{-1}(0.4)\\\\\Rightarrow m\angle XYZ=66.4^\circ.$

Thus, the required measure of angle XYZ is 66.4°.

Answer 2

Applying trigonometry ratio, the measure of angle XYZ in triangle XYZ, to 1 decimal place is $66.4^{\circ}$

• We need to apply trigonometry ratio formula in finding the size of angle XYZ in right triangle XYZ.

Recall:

• The trigonometry ratios are denoted with the acronym, SOHCAHTOA.

Given:

• angle XYZ = $\theta$
• Hypotenuse = 15 cm
• Adjacent = 6 cm

• The trigonometry ratio we would apply is CAH. Which is:

$Cos \theta = \frac{Adjacent}{Hypotenuse}$

• Plug in the values

$Cos \theta = \frac{6}{15} = 0.4\\\\\theta = cos^{-1}(\frac{6}{15})\\\\\theta = 66.4^{\circ}$

Therefore, applying trigonometry ratio, the measure of angle XYZ in triangle XYZ, to 1 decimal place is $66.4^{\circ}$

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