Solve the right triangle, ΔABC, for all the missing side and angles to the nearest tenth given sides a = 10.6 and b = 19.2.

Accepted Solution

Answer:Part 1) [tex]c=21.9\ units[/tex]Part 2) [tex]B=61.1\°[/tex]Part 3) [tex]A=28.9\°[/tex]Part 4) [tex]C=90\°[/tex]Step-by-step explanation:step 1Find the length side cApplying the Pythagoras Theorem[tex]c^{2}=a^{2}+b^{2}[/tex]substitute the given values[tex]c^{2}=10.6^{2}+19.2^{2}[/tex][tex]c^{2}=481[/tex][tex]c=21.9\ units[/tex]step 2Fin the measure of angle Bwe know thatIn the right triangle[tex]tan(B)=b/a[/tex]substitute the given values[tex]tan(B)=19.2/10.6[/tex][tex]B=arctan(19.2/10.6)=61.1\°[/tex]step 3Find the measure of angle Awe know thatThe measure of interior angles in a triangle must be equal to 180 degreesso∠A+∠B+∠C=180°Remember that in a right triangle the measure of angle C is 90 degreeswe have[tex]B=61.1\°[/tex][tex]C=90\°[/tex]substitute[tex]A+61.1\°+90\°=180\°[/tex][tex]A=28.9\°[/tex]