How do you find the measure of each of the angles of a triangle given the measurements of the sides are 7, 24, 25?

Question

19597 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-09T01:43:42

$color(green)(hat A = 16.26^@, hat B = 73.74^@, hat C = 90^@$

Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides

![https://byjus.com/maths/pythagoras-theorem/]( useruploads.socratic.org )

Given $a = 7, b = 24, c = 25$

$a^2 + b^2 = 7^2 + 24^2 = 625 = c^$

Hence it's a right triangle with $hat C = pi/2 = 90^@$

![http://www.gradeamathhelp.com/http://trigonometry.html](https://useruploads.socratic.org/rCn5I5bfSXKTAjEV78Ry_trigonometry%20functions.png)

$sin A = (opp)/ (hyp) = b/c = 7 / 25$

$hat A = sin^-1 (7/25) = 0.2838^c or 16.26^@$

$:. hat B = pi - pi/2 - 0.2838 = 1.287^c or = 73.74^@$

$color(red)("Verification : ")sin B = ( opp) / (hyp) = 24 / 25$

$hat B = sin ^-1(24/25) = 1.287^c or = 73.74^@$