Trigonometry Practise

from the figure as shown. tan(10) = h / d

tan(15) = (2000 - h) / d Solve for d the last 2 equations as follows

d = h / tan(10) and d = (2000 - h) / tan(15) and eliminate d as follows

h / tan(10) = (2000 - h) / tan(15) Solve the above for h

h = 2000 tan(10) / [ tan(15) + tan(10)]

= 793.8 m

let $x$ be the horizontal distance from the viewer to the mountain.

$\tan 10 = \frac{h}{x}$

$\tan 15 = \frac{2000 - h}{x}$

equate the values of $x$ and solve for $h$

$\frac{h}{\tan 10} = \frac{200 - h}{\tan 15}$

$h = \boxed{793.77}$

$\tan 15=\dfrac{2000-h}{x}$ or $x \tan 15=2000-h$ $\color{plum}(1)$

$\tan 80 = \dfrac{x}{h}$ or $x=\tan 80$ $\color{plum}(2)$

Substitute $\color{plum}(2)$ in $\color{plum}(1)$ . We have

$h \tan 80(\tan 15)=2000-h$

$h+1.5196h=2000$

$2.5196h=2000$

$h\approx$ $\boxed{793.8}$

793.771 :D :D