Question

Item 23 Solve the triangle with values a=23, b=24, and c=20. Round decimal answers to the nearest tent

Answer 1

Answer:

Part 1) $\angle\ C=50.3\°$

Part 2) $\angle\ B=67.4\°$

Part 3) $\angle\ A=62.3\°$

Step-by-step explanation:

step 1

Find the measure of angle C

Applying the law of cosines

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

substitute the given values and solve for cos(C)

$20^{2} =23^{2} +24^{2} -2(23)(24)cos(C)$

$2(23)(24)cos(C)=23^{2} +24^{2} -20^{2}$

$1,104cos(C)=705$

$cos(C)=705/1,104$

$C=arccos(705/1,104)=50.3\°$

step 2

Find the measure of angle B

Applying the law of cosines

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

substitute the given values and solve for cos(B)

$24^{2} =20^{2} +23^{2} -2(20)(23)cos(B)$

$2(20)(23)cos(B)=20^{2} +23^{2} -24^{2}$

$920cos(B)=353$

$cos(B)=353/920$

$B=arccos(353/920)=67.4\°$

step 3

Find the measure of angle A

Remember that the sum of the internal angles of triangle must be equal to 180 degrees

$\angle\ A+\angle\ B+\angle\ C=180\°$

substitute the given values and solve for ∠A

$\angle\ A+67.4\°+50.3\°=180\°$

$\angle\ A=180\°-117.7\°$

$\angle\ A=62.3\°$