Answer:
1) [tex]b=12[/tex]
2) [tex]tan(22.6\°)=\frac{a}{12}[/tex] (Third option)
Step-by-step explanation:
Remember that:
[tex]cos\alpha=\frac{adjacent}{hypotenuse}\\\\tan\alpha=\frac{opposite}{adjacent}[/tex]
1) Given that:
[tex]cos(22.6\°)=\frac{b}{13}[/tex]
You know that b is the adjacent side of the right triangle.
To solve for b you must multiply both sides of the expression by 13. Then, the value of b is:
[tex]13*cos(22.6\°)=\frac{b}{13}*13\\13*cos(22.6\°)=b\\b=12[/tex]
2) Then, you have that the equation correctly uses the value of b ( adjacent side) to solve for a (opposite side) is:
[tex]tan(22.6\°)=\frac{a}{12}[/tex]
The value for b is 12 and [tex]tan(22.6 ^{\circ \:} )=\frac{a}{12}\\[/tex].
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º.
For solving this question, you need to apply trigonometric ratios for the right triangle.
This question informs [tex]cos (22.6)=\frac{b}{13}[/tex]. Here, you should remember that cos of an angle is calculated by the ratio between the adjacent side from the angle and the hypotenuse of the right triangle. Therefore, [tex]cos=\frac{adj}{hyp}[/tex].
From a calculator, you find cos(22.6°)=0.92321. Thus,
[tex]cos (22.6)=\frac{b}{13}\\ \\ 0.92321=\frac{b}{13}\\ \\ b= 0.92321*13\\ \\ b=12.002\\ \\ b=12[/tex]
The second part of question asks how to find the tangent value. The tangent can be calculated by formula presented below:
[tex]tan(\alpha )=\frac{opposite \;side\;angle}{adjacent\;side\;angle}[/tex]
For the angle 22.6°, you have:
Therefore, [tex]tan(22.6 ^{\circ \:} )=\frac{a}{12}\\[/tex]
Learn more about the trigonometric ratios here:
brainly.com/question/11967894
