Question

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

Answer 1

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

Answer 2

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)