find m∠y.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nm∠y = °
find m∠y.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nm∠y = °
Answer
Explanation:
Step1: Use trigonometric ratio
In right - triangle ( \triangle XYZ) with ( \angle X = 90^{\circ}), we know the adjacent side to ( \angle Y) is (XY = 5) and the hypotenuse (YZ) can be found using Pythagoras' theorem (YZ=\sqrt{5^{2}+7^{2}}=\sqrt{25 + 49}=\sqrt{74}), but we can also use the tangent function. (\tan Y=\frac{opposite}{adjacent}). Here, (\tan Y=\frac{XZ}{XY}) (opposite side to (Y) is (XZ = 7), adjacent side to (Y) is (XY = 5)). So, (\tan Y=\frac{7}{5}).
Step2: Find the angle
We know that if (\tan Y=\frac{7}{5}), then (Y=\arctan(\frac{7}{5})). Using a calculator, (Y=\arctan(1.4)\approx54.5^{\circ}).
Answer:
(54.5)