Question

m and or the timiz iane shown n t r 5.10 m.) ngle shown in the figure below, what are each of the following? (Let y 4.50 le (a) the length (in m) of the unknown side x (b) the tangent of e (c) the sine of ф (d) What if? Keeping the length found in (a) fixed, by what factor would the length of the 4.50 m side have to be changed for the angles and ф to be equal? (Let y, be the new length of the 4.50 m side.)

Answer 1

(a) Using Pythagoras Theorem : $x^2 + y^2 = r^2$

x = $\sqrt{r^2 - y^2}$ = 2.36 m

(b) tangent ($\theta$) = height/base = y/x = 4.5/2.36 = 1.90

(c) sine ($\phi$) = x/r = 2.36/5.1 = 0.46

(d) x = 2.36 m,

if $\theta = \phi$ .

For right angled triangle one of the angle is 90 degees.

and two angles are equal. As we know sum of the angles is 180 degrees.

So, $\theta +\phi + 90 = 180$

$\theta = 45$

tan($\theta$) = tan(45) = 1

x = y

y = 2.36

y'/y = 2.36/4.5 = 0.524.