1. ## math help

hi I need major help in trig there is only 4 questions so yeah any help would be VERY helpful to me! thanks!

2. Hello, Justin!

Here's #1 . . .

In the triangle shown, $AC = 194$ cm.
What is the length of $BD$ to the nearest cm?
Code:
                                          * D
*   * |
*       *45°|
*           *     |
*               *       |
* 15°             B *         |
A *-----------------------*-----------* C
: - - - - - - - 194 - - - - - - - - :

In right triangle $DCA\!:\;\;\tan 15^o \:=\:\frac{CD}{AC}$

. . Then: . $CD \:=\:AC\tan15^o \:=\:194\cdot\tan15^o\quad\Rightarrow\quad CD \:\approx\:51.98$

In right triangle $DCB\!:\;\;\cos45^o = \frac{CD}{BD}\quad\Rightarrow\quad BD \:=\:\frac{CD}{\cos45^o}$

. . Therefore: . $BD \:=\:\frac{51.98}{\cos45^o} \:=\:73.51082097\quad\Rightarrow\quad\boxed{BD \:\approx\: 74\text{ cm}}$