Question

1. what is the tangent ratio of angle y?

m to n is 15 ft, n to o is 8 ft, m to o is 17 ft, angle at n is right angle, angle at m is x, angle at o is y

Explanation:

Step1: Recall tangent ratio definition

In a right triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. For angle \( y \), we need to identify the opposite and adjacent sides.

Step2: Identify sides for angle \( y \)

In right triangle \( MNO \) (right - angled at \( N \)), for angle \( y \) (at vertex \( O \)):

• The side opposite to angle \( y \) is \( MN \) with length \( 15\space ft \).
• The side adjacent to angle \( y \) is \( ON \) with length \( 8\space ft \).

Step3: Calculate tangent ratio

Using the formula for tangent, \( \tan(y)=\frac{\text{opposite}}{\text{adjacent}}=\frac{MN}{ON} \). Substituting the values \( MN = 15\space ft \) and \( ON=8\space ft \), we get \( \tan(y)=\frac{15}{8} \).

Answer:

\(\frac{15}{8}\)