Solve the right triangle, ΔABC, for the missing sides and angle to the nearest tenth given angle B = 27° and side c = 15.

Accepted Solution

Answer:Part 1) [tex]C=90\°[/tex]Part 2) [tex]A=63\°[/tex]Part 3) [tex]b=6.8\ units[/tex]Part 4) [tex]a=13.4\ units[/tex]Step-by-step explanation:step 1Find the measure of angle Cwe know thatThe triangle ABC is a right trianglesoAngle C is a right angletherefore[tex]C=90\°[/tex]step 2Fin the measure of angle Awe know thatIn the right triangle ABC ∠B+∠A=90° -----> by complementary angleswe have[tex]B=27\°[/tex]substitute[tex]27\°+A=90\°[/tex][tex]A=63\°[/tex]step 3Find the length side bwe know thatIn the right triangle ABC[tex]sin(B)=b/c[/tex][tex]b=(c)sin(B)[/tex]substitute the given values[tex]b=(15)sin(27\°)=6.8\ units[/tex]step 4Find the length side awe know thatIn the right triangle ABC[tex]sin(A)=a/c[/tex][tex]a=(c)sin(A)[/tex]substitute the given values[tex]a=(15)sin(63\°)=13.4\ units[/tex]