Question

solve the triangle.$a=35^{\circ },b=5,c=8$what is the length of side a?select the correct choice below and, if necessary, fill in the answer box to complete your choice.a. $a=\square$ (round to the nearest tenth as needed.)b. there is no solution.help me solve this view an example get more helpclear all

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines for side $a$ is $a^2 = b^2 + c^2 - 2bc\cos(A)$. Substitute $b=5$, $c=8$, $A=35^\circ$.
$a^2 = 5^2 + 8^2 - 2(5)(8)\cos(35^\circ)$

Step2: Calculate each term

Compute squares and product:
$5^2=25$, $8^2=64$, $2(5)(8)=80$, $\cos(35^\circ)\approx0.8192$
$a^2 = 25 + 64 - 80(0.8192)$

Step3: Simplify the expression

Sum and subtract:
$25+64=89$, $80(0.8192)=65.536$
$a^2 = 89 - 65.536 = 23.464$

Step4: Solve for $a$

Take square root of the result:
$a = \sqrt{23.464} \approx 4.8$

Answer:

A. $a=4.8$