Question

Express x in terms of the other variables in the diagram below:

Answer 1

For the answer to the question above, just use similar triangles. 
Here's the equations that I used.

t/h = (x + t) / r 
x + t = rt / h 
x = rt / h - t 
I hope my answer helped you in your problem, Have a nice day

Answer 2

From the diagram below , x = t ( r - h ) / h

Further explanation

Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

sin ∠A = opposite / hypotenuse

cos ∠A = adjacent / hypotenuse

tan ∠A = opposite / adjacent

There are several trigonometric identities that need to be recalled, i.e.

$cosec ~ A = \frac{1}{sin ~ A}$

$sec ~ A = \frac{1}{cos ~ A}$

$cot ~ A = \frac{1}{tan ~ A}$

$tan ~ A = \frac{sin ~ A}{cos ~ A}$

Let us now tackle the problem!

Look at ΔADE in the attachment.

We will use the following formula to find relationship between variable t and h:

tan ∠A = opposite / adjacent

$\tan \angle A = \frac{DE}{AD}$

$\large {\boxed{ \tan \angle A = \frac{h}{t} } }$ → Equation 1

Look at ΔABC in the attachment.

We will use the following formula to find relationship between variable r , t and x:

tan ∠A = opposite / adjacent

$\tan \angle A = \frac{BC}{AB}$

$\large {\boxed{ \tan \angle A = \frac{r}{x + t} } }$ → Equation 2

Next we can substitute equation 1 to equation 2 :

$\tan \angle A = \frac{r}{x+t}$

$\frac{h}{t} = \frac{r}{x+t}$

$(x + t)h = r ~ t$

$(x + t) = \frac{(r ~ t)}{h}$

$x = \frac{(r ~ t)}{h} - t$

$x = \frac{(r ~ t)}{h} - \frac{(h ~ t)}{h}$

$\large {\boxed {x = \frac{t(r - h)}{h}} }$

Learn more

• Calculate Angle in Triangle : brainly.com/question/12438587
• Periodic Functions and Trigonometry : brainly.com/question/9718382
• Trigonometry Formula : brainly.com/question/12668178

Answer details

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle