Use triangle ABC drawn below & only the sides labeled. Find the side of length AB in terms of side a, side b & angle C only. You will need to use both Soh-Cah-Toa and the Pythagorean Theorem to solve for side AB.

Step-by-step explanation:

Given:

The above triangle

Required

Solve for AB in terms of a, b and angle C

Considering right angled triangle BOC where O is the point between b-x and x

From BOC, we have that:

Make h the subject:

Also, in BOC (Using Pythagoras)

Make the subject

Substitute for h

becomes

Factorize

In trigonometry:

So, we have that:

Take square roots of both sides

In triangle BOA, applying Pythagoras theorem, we have that:

Open bracket

Substitute and in

Open Bracket

Reorder

Factorize:

In trigonometry:

So, we have that:

Take square roots of both sides

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

e^-kt = n/n0 = 0.79  

-kt = ln 0.79  

t = - ln 0.79/0.0001  

= 2357 years

step-by-step explanation: