# Right angled triangle help

• Jan 10th 2007, 12:39 AM
Kim2425
Right angled triangle help
Ok, I have a few questions I need some help with please!

using a right angled triangle ABC where B = 90 degrees find

A)BC
B)AB

if

i) AC = 10cm and A =32 degrees
ii) AC = 12cm and A = 46 degrees
iii) AC = 6cm and C = 42 degrees

:confused:
• Jan 10th 2007, 04:53 AM
earboth
Quote:

Originally Posted by Kim2425
...
using a right angled triangle ABC where B = 90 degrees find
A)BC
B)AB

if

i) AC = 10cm and A =32 degrees
ii) AC = 12cm and A = 46 degrees
iii) AC = 6cm and C = 42 degrees
...

Hello,

use the definitions of Sine or Cosine. With your triangle:

$\sin(A)=\frac{\overline{BC}}{\overline{AC}}$

$\cos(A)=\frac{\overline{AB}}{\overline{AC}}$

Now use the given values to calculate the missing one:

to i)
$\overline{BC}=\overline{AC} \cdot \sin(A) \approx 5.3 \ cm$
$\overline{AB}=\overline{AC} \cdot \cos(A) \approx 8.48 \ cm$

to ii)
$\overline{BC}=\overline{AC} \cdot \sin(A) \approx 8.63 \ cm$
$\overline{BC}=\overline{AC} \cdot \sin(A) \approx 8.34 \ cm$

to iii)

90° - C = A = 48°. Use the formulas as above:

$\overline{BC}=\overline{AC} \cdot \sin(A) \approx 4.46 \ cm$
$\overline{BC}=\overline{AC} \cdot \sin(A) \approx 4.01 \ cm$

EB