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For triangle HJK, j = 31, m∠H = 132 degrees, m∠J = 21 degrees, and m∠K = 27 degrees. Find h to the nearest whole number.

Guest Feb 2, 2015

Best Answer 

 #1
avatar+20040 
+10

For triangle HJK, j = 31, m∠H = 132 degrees, m∠J = 21 degrees, and m∠K = 27 degrees. Find h to the nearest whole number.

$$\small{\text{
$
\tan{(132)}=\frac{h}{p} \qquad
\tan{(27)}=\frac{h}{q} \qquad p+q=31\ m
$
}}\\
\small{\text{
$
p=\frac{h}{\tan{(132)}} \qquad
q=\frac{h}{\tan{(27)}} \qquad \frac{h}{\tan{(132)}} +\frac{h}{\tan{(27)}}=31\ m
$
}}\\
\small{\text{
$
h* \left(
\frac{1}{\tan{(132)}} + \frac{1}{\tan{(27)}}
\right)=31\ m
$
}}\\
\small{\text{
$
h* \left(
-0.90040404430 + 1.96261050551
\right)=31\ m
$
}}\\
\small{\text{
$
h*1.06220646121 =31\ m
$
}}\\
\small{\text{
$
h =\frac{31}{1.06220646121}\ m = 29.1845334520\ m
$
}}\\
\small{\text{
h to the nearest whole number:
$
h = 29\ m
$
}}$$

heureka  Feb 3, 2015
 #1
avatar+20040 
+10
Best Answer

For triangle HJK, j = 31, m∠H = 132 degrees, m∠J = 21 degrees, and m∠K = 27 degrees. Find h to the nearest whole number.

$$\small{\text{
$
\tan{(132)}=\frac{h}{p} \qquad
\tan{(27)}=\frac{h}{q} \qquad p+q=31\ m
$
}}\\
\small{\text{
$
p=\frac{h}{\tan{(132)}} \qquad
q=\frac{h}{\tan{(27)}} \qquad \frac{h}{\tan{(132)}} +\frac{h}{\tan{(27)}}=31\ m
$
}}\\
\small{\text{
$
h* \left(
\frac{1}{\tan{(132)}} + \frac{1}{\tan{(27)}}
\right)=31\ m
$
}}\\
\small{\text{
$
h* \left(
-0.90040404430 + 1.96261050551
\right)=31\ m
$
}}\\
\small{\text{
$
h*1.06220646121 =31\ m
$
}}\\
\small{\text{
$
h =\frac{31}{1.06220646121}\ m = 29.1845334520\ m
$
}}\\
\small{\text{
h to the nearest whole number:
$
h = 29\ m
$
}}$$

heureka  Feb 3, 2015
 #2
avatar+27062 
+5

I think the sine rule might be the simplest approach here:

h/sin(H) = j/sin(J)

 

$${\mathtt{h}} = {\frac{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{132}}^\circ\right)}{\mathtt{\,\times\,}}{\mathtt{31}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{21}}^\circ\right)}}} \Rightarrow {\mathtt{h}} = {\mathtt{64.284\: \!458\: \!526\: \!596\: \!557\: \!1}}$$

 

or h = 64 to the nearest whole number

 

triangle

 

I've assumed h is opposite angle H, j is opposite angle J etc.

.

Alan  Feb 3, 2015

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