Answer:
[tex]a\approx7.2[/tex]
Step-by-step explanation:
The given problem presents one with the following information:
- Triangle ABC
- Side (b) has a measure of (13.5)
- Side (c) has a measure of (8.9)
- Angle (A) has a measure of (29)
To solve this problem, one can use the law of cosines. The law of cosines is a property that can apply to any triangle. This property comes in the form of a formula, which is as follows:
[tex]a^2=\sqrt{b^2+c^2-2bc(cos(A))}[/tex]
Where (a), (b), and (c) are sides of the triangle, and (<A) is the angle opposite the side (a).
Substitute the given information into the formula and solve for the unknown side (a):
[tex]a=\sqrt{b^2+c^2-2bc(cos(A))}[/tex]
[tex]a=\sqrt{(13.5)^2+(8.9)^2-2(13.5)(8.9)(cos(29))}[/tex]
Simplify,
[tex]a=\sqrt{(13.5)^2+(8.9)^2-2(13.5)(8.9)(cos(29))}[/tex]
[tex]a=\sqrt{182.25+79.21-240.3(cos(29))}[/tex]
[tex]a=\sqrt{261.46-240.3(cos(29))}[/tex]
[tex]a=\sqrt{261.46-210.1711}[/tex]
[tex]a=\sqrt{51.2889}[/tex]
[tex]a\approx7.2[/tex]
