Trigonometry...totally lost...any help out there?

Question

this is the question...i have no idea what i am supposed to do right now for it!

"in triangle ABC, measurement of angle C is 90degrees, tangent of angle A=.7, and line AC=40. Find line BC"

if possible, can you explain how to get the answer or show the steps or something?!?! any help is great!
please and thank you!!!!!!!!!

Answer 1

You have a right triangle (obviously, otherwise it wouldn't be trig). Angle C is 90 deg and is made up of vertex C and line segments AC and BC. Call the hypotenuse AB. Tangent of A is 0.7. Tangent is sine divided by cosine, or the length of the leg opposite the angle divided by the length of the leg adjacent to the angle. In this case, you know the length of the adjacent leg. Solve for the opposite.

0.7=BC/40
BC=28

Further clarification: A right triangle has 2 legs, a hypotenuse and 3 angles. There is one 90 deg angle and 2 acute angles. When applying trig functions we refer to opposite and adjacent sides. This only applies to the acute angles. Each angle is made up of 2 line segments. One of the segments is always the hypotenuse. The other is the adjacent side. The opposite side is the third side of the triangle. One way to remember is that if you picture the angle as a mouth, it is "eating" the opposite side.

Answer 2

OK I can't draw a triangle, so you will have to visualize a right triangle with angle C = 90 degrees. |_\ or something like that. They tell us what the angle A is by giving the tangent. Tangent of an angle is equal to the ratio of the side opposite over the side adjacent. Tan A = length BC / Length AC = 0.7. In a calculator, Tan -1 of 0.7 = 35 degrees. Now in a right triangle all angles add up to 180. So 180 - 90 -35 = 55. Angle B is therefore 55 degrees. Sine is defined as the ratio of BC to the Hypotenuse AB. The length of AB = 40. Sine 35 = BC/40. 40*sine35 = 28.

Answer 3

Angle C being 90 degrees, you have a right triangle, and the other two angles will add up to 90 degrees, there being 180 degrees in all triangles.
To remember the trig functions: sine, cosine, and tangent, remember this -
"Oscar had
A handful
Of apples."
Oscar had = opposite/hypotenuse=sine
A handful = adjacent/hypotenuse=cosine
of apples = opposite/adjacent=tangent
Draw a right triangle with C the 90 degree (right) angle, and A and B the others. Line AC=40
The tangent of angle A is 0.7, and line AC is adjacent
(next to) angle A.
The tangent is the side opposite over the side adjacent.
We can now set up an equation with x as the unknown line BC (opposite side of angle A).
x/40=0.7 using the tangent definition.
Multiplying through by 40 we get
x= 0.7(40)=28
BC=28

Answer 4

The tangent of angle in a right triangle is the length of the opposite leg divided by the length of the adjacent leg.
For your triangle, since C is the right angle, the legs are AC and BC. The opposite leg to A is BC and the adjacent leg is AC. Then tanA = BC/AC = 0.7. Since AC = 40, BC/40 = 0.7. So BC = 28.

Answer 5

Sorry, I couldn't understand it then, and I certainly don't remember any of it now...the only thing I can say for sure is that you really won't need it later on, unless you plan on engineering for a career choice.