SOLUTION: What is the area of a right triangle when the hypotenuse is 5 cm long and one angle is pi/10 ?

Question 839668: What is the area of a right triangle when the hypotenuse is 5 cm long and one angle is pi/10 ?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
see the following diagram:
$$$

A is your angle.
sine(A) is equal to a/c.
cosine(A) is equal to b/c.

solve for a and b and you get:

a = c * sine (A)
b = c * cosine (A)

a is the height of your triangle.
b is the base of your triangle.

the area of the triangle is equal to 1/2 * base * height which becomes:

area of the triangle is equal to 1/2 * b * a which becomes:

area of the triangle is equal to 1/2 * c * cosine (A) * c * sine (A).

this can be simplified to:

area of the triangle is equal to 1/2 * c^2 * cosine (A) * sine (A).

replace c with 5 and replace A with pi/10 and you get:

area of the triangle is equal to 1/2 * 5^2 * cosine (pi/10) * sine (pi/10).

use your calculator to find sine and cosine (pi/10). the angle should be in radians. if you want to work in degrees, then convert angle in radians to angle in degrees by multiplying the angle in radians by 180 / pi. you will get pi/10 * 180 / pi = 18 degrees.

anyway, regardless of whether you are working in degrees or radians, you will get:

area of the triangle is equal to 1/2 * 25 * .951056516 * .309016994 which is equal to 3.673657827 which you can round to 3.67

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