Question

1. which of the following is the ratio for sina?

a. $\frac{15}{17}$
b. $\frac{8}{17}$
c. $\frac{15}{8}$
d. $\frac{8}{15}$

1. $\frac{15}{8}$ is the value of which of the following?

a. sinc
b. cosc
c. tanc
d. tana

Explanation:

Question 1:

Step1: Recall Sine Definition

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle A$, the opposite side to $\angle A$ is $BC = 15$, and the hypotenuse is $AC = 17$.

Step2: Apply Sine Formula

So, $\sin(A) = \frac{\text{opposite to } A}{\text{hypotenuse}} = \frac{15}{17}$.

Step1: Recall Trigonometric Ratios

• $\sin(C) = \frac{\text{opposite to } C}{\text{hypotenuse}} = \frac{AB}{AC} = \frac{8}{17}$
• $\cos(C) = \frac{\text{adjacent to } C}{\text{hypotenuse}} = \frac{BC}{AC} = \frac{15}{17}$
• $\tan(C) = \frac{\text{opposite to } C}{\text{adjacent to } C} = \frac{AB}{BC} = \frac{8}{15}$
• $\tan(A) = \frac{\text{opposite to } A}{\text{adjacent to } A} = \frac{BC}{AB} = \frac{15}{8}$

Step2: Match the Ratio

We are given the ratio $\frac{15}{8}$, which matches the value of $\tan(A)$.

Answer:

a. $\boldsymbol{\frac{15}{17}}$

Question 2: