Thread: Trigonometry problem

1. Trigonometry problem

Not sure how to do this problem:

Find the other side and angle measures for the given right triangle:
Name: HPJ
Right Angle: H
Given Data: m<J =29°51', j = 4651

Thanks a lot.

2. Hello,Trentt!

Find the other sides and angles.
Triangle $\displaystyle PHJ$
Right Angle: $\displaystyle H$
Given data: .$\displaystyle \angle J = 29^o51',\;j = 4651$
Code:
      P
*
|  *
|     *  h
4651 |        *
|           *
|       29.85°-*
* - - - - - - - - *
H        p          J
We know that: .$\displaystyle \angle H = 90^o$

We have: .$\displaystyle \angle J \:=\:29^o51' \:=\:29 +\frac{51}{60} \:=\:29.85^o$

Then: .$\displaystyle \angle P \:=\:90^o - 29.85^o \:=\:60.15^o$

We have: .$\displaystyle \begin{array}{ccccccc}J & = & 29.85^o & \qquad & k & = & 4651 \\ P & = & \boxed{60.15^o} & & p & = & \boxed{\qquad} \\ H & = & \boxed{90.00^o} & & h & = & \boxed{\qquad} \end{array}$

$\displaystyle \tan P \:= \:\frac{p}{j}\quad\Rightarrow\quad p \:= \:j\!\cdot\tan P \:=\:4651\!\cdot\!\tan60.15^o \:\approx\:8104.7$

$\displaystyle \sin J \:=\:\frac{j}{h}\quad\Rightarrow\quad h \:=\:\frac{j}{\sin J} \:=\:\frac{4651}{\sin29.85^o} \:\approx\:9344.4$

Therefore: .$\displaystyle \begin{array}{ccccccc}J & = & 29.85^o & \qquad & k & = & 4651.0 \\ P & = & \boxed{60.15^o} & & p & = & \boxed{8104.7} \\ H & = & \boxed{90.00^o} & & h & = & \boxed{9344.4} \end{array}$