Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your
what are the values of sin x and tan y in the triangle below?
triangle image with hypotenuse √34, leg xz=5, leg yz=3, right-angled at z
options:

• sin x = 5/√34, tan y = 3/5
• sin x = 3/√34, tan y = 5/3
• sin x = 5/√34, tan y = 5/3
• sin x = 3/√34, tan y = 3/5

Explanation:

Step1: Recall Trigonometric Ratios

For a right triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Find \(\sin X\)

In \(\triangle XYZ\), \(\angle Z = 90^\circ\), hypotenuse \(XY=\sqrt{34}\), opposite side to \(\angle X\) is \(YZ = 3\). So \(\sin X=\frac{YZ}{XY}=\frac{3}{\sqrt{34}}\).

Step3: Find \(\tan Y\)

For \(\angle Y\), opposite side is \(XZ = 5\), adjacent side is \(YZ = 3\). So \(\tan Y=\frac{XZ}{YZ}=\frac{5}{3}\).

Answer:

\(\sin X=\frac{3}{\sqrt{34}},\tan Y=\frac{5}{3}\) (the second option among the given choices)