use the diagram of triangle xyz to answer the questions. what is the length of side xy? what is the value of…

Explanation:

Step1: Find length of XY using Pythagorean theorem

In right - triangle XYZ with legs YZ = 8 and XZ = 6, by the Pythagorean theorem (a^{2}+b^{2}=c^{2}), where (c) is the hypotenuse (XY). So (XY=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10).

Step2: Define sine of angle X

(\sin(X)=\frac{\text{opposite}}{\text{hypotenuse}}). The opposite side to angle (X) is (YZ = 8) and the hypotenuse is (XY = 10), so (\sin(X)=\frac{8}{10}=\frac{4}{5}).

Step3: Define cosine of angle X

(\cos(X)=\frac{\text{adjacent}}{\text{hypotenuse}}). The adjacent side to angle (X) is (XZ = 6) and the hypotenuse is (XY = 10), so (\cos(X)=\frac{6}{10}=\frac{3}{5}).

Step4: Define tangent of angle X

(\tan(X)=\frac{\text{opposite}}{\text{adjacent}}). The opposite side to angle (X) is (YZ = 8) and the adjacent side is (XZ = 6), so (\tan(X)=\frac{8}{6}=\frac{4}{3}).

Answer:

Length of side XY: 10 Value of (\sin(X)): (\frac{4}{5}) Value of (\cos(X)): (\frac{3}{5}) Value of (\tan(X)): (\frac{4}{3})