Answer: [tex]39.8^{\circ}[/tex]
Step-by-step explanation:
In the given picture , we have a right triangle.
Let x represents ∠XYZ.
The side opposite to angle x = 10 in.
The side adjacent to angle x = 12 in.
By trigonometry, we have
[tex]\tan x=\dfrac{\text{Side opposite to x}}{\text{Side adjacent to x}}[/tex]
[tex]\Rightarrow\tan x=\dfrac{10}{12}=0.833333333\\\\\Righatrrow\ x=\tan ^{-1}(0.83333333)=0.69473826[/tex]
In degrees, [tex]x=0.69473826\times\dfrac{180^{\circ}}{\pi}\approx39.8^{\circ}[/tex]
Hence, the best approximation for the measure of ∠XYZ is [tex]39.8^{\circ}[/tex]
