(07.02 lc) the picture below shows a right-triangle-shaped charging stand for a gaming system: the side face of a charging stand is a right triangle labeled abc. the measure of angle acb is 90 degrees and the measure of angle abc is 70 degrees. the height of the charging stand, ac, is 9 inches. which expression shows the length, bc, of the base of the stand?

since there are no choices given, i will give 2 answers using 2 methods.

1st method: using sine law

we are given the measurements of the angles and one side, therefore to solve this problem we can use the sine law to look for the length of another side, side bc.

where sine law is:

side bc / angle bac = side ac / angle abc

first let us calculate for angle bac. we know that the total angle of a triangle is 180 degrees, therefore:

angle bac = 180 – 70 – 90

angle bac = 20 degrees

going back to the sine law, we substitute the known values:

side bc /sin 20 = 9 / sin 70

side bc = 3.28 inches

2nd method: trigo function

we can also solve this problem by remembering that:

tan θ = opposite side / adjacent side

where,

θ = 70 degrees

opposite side = side ac = 9 inches

adjacent side = side bc

therefore,

tan 70 = 9 / side bc

side bc = 9 / tan 70 = 9 cot 70 = 3.28 inches

we can arrive at the same answer using the 2 methods.