The triangle △ABC is right-angled with right angle at corner C and angle α (alpha) at corner A. Calculate the area of the triangle, given that c=|AB|=10, and that tan α(alpha) =3/7.

Answer 1

Given:

c = |AB| = 10

tan(a) = 3/7

Using Pythagorean theorem and the leg ratio

we can determine the relative hypotenuse length.

c' = √3² + 7²

c' =√58

But since the actual length of c = 10, the 3 lengths of

a, b and c need to be scaled up by a factor of:

s. f. = c/c' = 10/√58 =

The leg lengths a & b are:

a = 3(10/√58)

b = 7(10/√58)

And the area is:

Answer 2

tanA = 3/7

angle A = tan^-1(3/7) = about 23.2 degrees

c=|AB| = 10

c^2 = a^2 + b^2, where the small letters are the sides opposite the angles with the capital letters

10^2 = a^2 +b^2 =100

a=3x, b=7x

9x^2 +49x^2 = 100

x^2 = 100/58 = 50/29

x = sqr(50/29) = 5sqr(2/29

a = 15sq(2/29)

b = 35sqr(2/29)

Area = ab/2 = 15(35)(2/29)/2

=525/29

= 18 3/29

= about 18.103

a = about 3.94

b = about 9.19

C = 90 degrees

A = about 23.2 degrees

B - 90-23.2 = about 66.8 degrees