Question

Find the tangent of each angle that is not the right angle.

Drag and drop the numbers into the boxes to show the tangent of each angle.

Answer 1

Explanation:

remember,

tan(x) = sin(x)/cos(x)

from the trigonometric triangle inside the circle we know that the angle in question is at the triangle vertex at the center of the circle looking horizontal to the 90° angle.

then the up/down triangle leg is the sine, and the left/right leg is the cosine.

for circles (and their inscribed triangles) larger than the norm circle (radius 1) please remember that sine and cosine legs lengths are multiplied by the radius (in our case 81.5).

so, for the angle at A that is easy :

sin(A) × 81.5 = 32

cos(B) × 81.5 = 75

tan(A) = sin(A)×81.5 / (sin(B)×81.5) = 32/75 =

= 0.426666666... ≈ 0.43

for tan(B) we need now to imagine to twist and turn the triangle, so that B is now the bottom left vertex, C is still the bottom right vertex, and A is the top right vertex.

and the we see

sin(B) × 81.5 = 75

cos(B) × 81.5 = 32

tan(B) = sin(B)×81.5 / (cos(B)×81.5) = 75/32 =

= 2.34375 ≈ 2.34

Answer 2

tan A = 0.43

tan B = 2.34

Explanation:

"tangent" is a trig ratio. If you have a right triangle, then you can do right triangle trigonometry.



First, let's look at a right triangle. The longest side is opposite the right angle (square angle, 90° angle it's marked with a little square) that is called the hypotenuse. You need hypotenuse for sine and cosine. So we won't use hypotenuse today (still good to know tho')

 Then there are the two legs of the right triangle. They make up the right angle. If you are standing at one of the smaller angles one of the legs is just beside you, making up the angle. The other leg is way across the triangle on the opposite side of the triangle.

So from angle A, the 32 is the OPPOSITE side. And the 75 is the leg right next to angle A. "Right next to" is called ADJACENT. The 75 is the ADJACENT side.

Tangent is the ratio of the OPPOSITE side to the ADJACENT side.

Like this:

tan A = OPP/ADJ

tan A = 32/75

tan A = 0.426666...

rounding, we get:

tan A = 0.43

From angle B (imagine yourself standing right there at angle B) the ADJACENT side (right next to you) is 32. And the OPPOSITE side is 75

Now the tangent ratio is slightly different--

tan B = OPP/ADJ

tan B = 75/32

tan B = 2.34375

rounding,

tan B = 2.34