Solve angle ABC by using the measurements angle ABC = 90°, angle BAC = 40°, and a = 10. Round measures of sides to thenearest tenth and measures of angles to the nearest degree.​

Accepted Solution

Answer:∠ACB==50°b=15.6 unitsc=11.9 unitsStep-by-step explanation:step 1Find the measure of angle BCAwe know thatThe sum of the interior angles of a triangle must be equal to 180 degrees∠ABC+∠BAC+∠ACB=180°substitute the given values90°+40°+∠ACB=180°∠ACB=180°-130°=50°step 2Find the measure of side bApplying the law of sinesa/sin(∠BAC)=b/sin(∠ABC)substitute the given values10/sin(40°)=b/sin(90°)b=10/sin(40°)b=15.6 unitsstep 3Find the measure of side cApplying the law of sinesc/sin(∠ACB)=a/sin(∠BAC)substitute the given valuesc/sin(50°)=10/sin(40°)c=[10/sin(40°)]*sin(50°)c=11.9 units