Chapter 11.CT, Problem 1CT

To determine

a

To express:

The ratio sin α in terms of a, b, and c.

Answer to Problem 1CT

Solution:

The value of sin α in terms of a, b, and c is sin α = $\frac{a}{c}$.

Explanation of Solution

Definition:

In a right triangle, the sine ratio for an acute angle is the ratio $\frac{oppsite side}{hypotenuse}$.

Given:

The right triangle shown below

From the figure given,

For the angle α, opposite side = a and hypotenuse = c.

By the definition, sin α = $\frac{oppsite side}{hypotenuse}$

sin α = $\frac{a}{c}$

Conclusion:

The value of sin α in terms of a, b, and c is sin α = $\frac{a}{c}$.

To determine

b.

To express:

The given tan β in terms of a, b, and c.

Answer to Problem 1CT

Solution:

The value of tan β in terms of a, b, and c is tan β = $\frac{b}{a}$.

Explanation of Solution

Definition:

In a right triangle, the tangent ratio for an acute angle is the ratio $\frac{oppsite side}{adjacent side}$.

Given:

The right triangle shown below

Calculation:

For the angle β, opposite side = b and adjacent side = a.

By the definition, tan β= $\frac{oppsite side}{adjacent side}$

tan β = $\frac{b}{a}$

Conclusion:

The value of tan β in terms of a, b, and c is tan β =$\frac{b}{a}$.