SOLUTION: How do I find the area of a right triangle where it gives me one leg and one angle in adition to the right? Say,the leg given is 16, opposite an angle 37 degrees? How do I find t

Algebra ->  Surface-area -> SOLUTION: How do I find the area of a right triangle where it gives me one leg and one angle in adition to the right? Say,the leg given is 16, opposite an angle 37 degrees? How do I find t      Log On


   

Question 592456: How do I find the area of a right triangle where it gives me one leg and one angle in adition to the right?
Say,the leg given is 16, opposite an angle 37 degrees?
How do I find the other leg and hypotonuse, then finding the area?
Found 2 solutions by Theo, jim_thompson5910:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you have a right triangle.
one angle other than the right angle.
one side opposite the angle.
you can use the sine function to get the hypotenuse or you can use the tan function to get the side opposite the other angle.
sine (37) = 16 / hypotenuse
multiply both sides of this equation by the hypotenuse and divide both sides of this equation by sine (37) to get:
hypotenuse = 16 / sine(37)
use your calculator to find the sine(37) and then solve for the hypotenuse.
similarly.
tangent (37) = 16 / side opposite the other angle.
multiply both sides of the equation side opposite the other angle and divide both sides of the equation by tangent (37) to get:
side opposite the other angle = 16 / tangent (37).
if you do this correctly, you will get:
hypotenuse = 26.58624226
side opposite the other angle = 21.23271715
to confirm you did this correctly, use the pythagorean formula to get:
(16)^2 + (21.23271715)^2 = (26.58624226)^2
this results in:
706.0282774 = 706.8282774 confirming the values for the hypotenuse and the other leg are good.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you are familiar with trigonometric functions.

In this case, you're going to use the sine function because

sin(angle) = opposite/hypotenuse


So plug in the given info to get

sin(37) = 16/h

now solve for the hypotenuse 'h'

sin(37) = 16/h

h*sin(37) = 16

h = 16/sin(37)

h = 26.58624


So the hypotenuse is roughly 26.58624 units.

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Now that you have the hypotenuse, you can use it to find the adjacent side (ie the other leg)

cos(angle) = adjacent/hypotenuse

cos(37) = x/26.58624

x = 26.58624*cos(37)

x = 21.2327


So the other leg is roughly 21.2327 units.

To find the area, use the formula

Area = (Base*Height)/2

A = (bh)/2


I'll let you compute the area. Let me know what you get.