In the triangle, bc=12 cm and tan c = 0.583. what is the length of the hypotenuse, to the nearest tenth of a centimeter

Given that BC=12 cm and tan C=0.583, the value of the hypotenuse will be given as follows:

BC is the adjacent, the height AB will be given by

AB/BC=tan C

thus

AB/12=0.583

AB=12*0.583

AB=6.996

hence using Pythagorean theorem:

c^2=b^2+a^2

thus;

c^2=6.996^2+12^2

c^2=192.944016

c=13.890~14 cm (to the nearest centimeter)

We have the following trigonometric relationship:

tan c = AB / BC

We cleared AB:

AB = BC * tan c

Substituting values:

AB = (12) * (0.583)

AB = 6,996

We now look for the hypotenuse using the Pythagorean theorem:

hypotenuse = root ((AB) ^ 2 + (BC) ^ 2)

Substituting values:

hypotenuse = root ((6,996) ^ 2 + (12) ^ 2)

hypotenuse = 13.9 cm

Answer:

The length of the hypotenuse, to the nearest tenth of a centimeter is:

hypotenuse = 13.9 cm