Question

Could anyone help me with this? Thanks in advance x

Answer 1

Answer:

find b: since the triangle is right angle triangle apply the Pythagorean theorem

c²+b²=d²

b²=d²-c²

b²=16²-12²

b²=256-144

b²=112

b=√112 = 4√7

the sum of the angle of the triangle=180

( in top Δ abd ) sin Ф=opp/hyp

sinФ=b/d=4√7/16= √7/4  radian

convert to degrees : √7/4 *180/π= 37.91 almost 38 degrees

which makes A= 38 degrees ( adjacent angles are equal when they have common side and do not overlap)

find a=?? apply law of cosine

a²= d^2 + c^2 − 2dc cosA

a²=16² + 12²-2(16)(12)cos38

a =√(16² + 12²-2(16)(12)cos38)

a=9.87 rounded to the nearest hundredth

(i hope it is right )