Q5 Q31.) Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find the value of each of the six trigonometric functions of theta.

See answers in bold below

Step-by-step explanation:

Using pythagoras theorem to find the unknown side a;

c² = a²+b²

a² = c²-b²

a² = 20²-16²

a² = 400 -256

a² = 144

a = √144

a = 12

for the six trigonometry functions;

According to SOH CAH TOA

sin theta = opposite/hypotenuse

Opposite = 12

Hypotenuse = 20

sin theta = 12/20

sin theta = 3/5

cos theta = adj/hyp

cos theta = 16/20

cos theta = 4/5

tan theta = opp/adj

tan theta = 12/16

tan theta = 3/4

cosec theta = 1/sintheta

cosec theta = 1/(3/5)

cosec theta = 5/3

sec theta = 1/cos theta

sec theta = 1/(4/5)

sec theta = 5/4

no

step-by-step explanation:

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!