Question

I need help with #5 please I have no idea how to do this

Answer 1

Answer:

tan theta = 3/4

cot theta  = 4/3

sin theta = 3/5

csc theta = 5/3

cos theta  4/5

sec theta =  5/4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

We know the adjacent side and the opposite side so we will use the tangent function

tan theta = opposite/ adjacent

tan theta = 6/8

tan theta = 3/4

cot theta = adjacent / opposite = 8/6 = 4/3

Now we need to find the hypotenuse, using the pythagorean theorem

a^2 + b^2 = c^2

6^2 + 8^2 = c^2

36+64 = c^2

100 =c^2

Taking the square root

sqrt(100) = sqrt(c^2)

10 = c

The hypotenuse = 10

sin theta = opposite / hypotenuse

sin theta = 6/10 = 3/5

csc theta = hypotenuse / opposite = 10/6 = 5/3

cos theta = adjacent/ hypotenuse = 8/10 = 4/5

sec theta = hypotenuse/adjacent = 10/8 = 5/4