Question

Find the size of angle XYZ.Give your answer to 1 decimal place.15 cm6 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

In your calculator type cos^-1 (6/15)

66.4 degrees

Hope this helps