Question

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Answer 1

Answer:

$a\approx7.2$

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:

$a^2=\sqrt{b^2+c^2-2bc(cos(A))}$

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):

$a=\sqrt{b^2+c^2-2bc(cos(A))}$

$a=\sqrt{(13.5)^2+(8.9)^2-2(13.5)(8.9)(cos(29))}$

Simplify,

$a=\sqrt{(13.5)^2+(8.9)^2-2(13.5)(8.9)(cos(29))}$

$a=\sqrt{182.25+79.21-240.3(cos(29))}$

$a=\sqrt{261.46-240.3(cos(29))}$

$a=\sqrt{261.46-210.1711}$

$a=\sqrt{51.2889}$

$a\approx7.2$

Answer 2

Answer:

7.2

Step-by-step explanation:

Apply Law of Cosines, given that b is 13.5, c is 8.9, and Angle a is 29.

${a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos(a)$

${a}^{2} = {13.5}^{2} + {8.9}^{2} - 2(13.5)(8.9) \times \cos(29)$

${a}^{2} = 182.25 + 79.21 - 240.3 \times 0.8746$

${a}^{2} = 182.25 + 79.21 - 210.1711$

$a = 7.2$