Question

Triangle ABC is a right triangle and cos(22.6o)=b/13. Solve for b and round to the nearest whole number. Which equation correctly uses the value of b to solve for a? tan(22.6o) = a/13 tan(22.6o) = 13/a tan(22.6o) = a/12tan(22.6o) =12/a

Answer 1

Answer:

Part 1) The value of b is $12\ units$

Part 2) $tan(22.6\°)=\frac{a}{12}$

Step-by-step explanation:

Part 1)

Find the value of b

In the right triangle ABC

Let

b-------> the adjacent side to angle 22.6°

a -----> the opposite side to angle 22.6°

13 ----> the hypotenuse of the right triangle ABC

we have

The cosine of angle 22.6° is equal to divide the adjacent side to angle 22.6° by the hypotenuse

$cos(22.6\°)=\frac{b}{13}$

Solve for b

Multiply both sides by 13

$b=(13)cos(22.6\°)=12\ units$

Part 2) Which equation correctly uses the value of b to solve for a?

we know that

In the right triangle ABC

The tangent of angle 22.6° is equal to divide the opposite side to angle 22.6° by the adjacent side to angle 22.6°

so

$tan(22.6\°)=\frac{a}{b}$

we have

$b=12\ units$

substitute

$tan(22.6\°)=\frac{a}{12}$