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

Apr 9, 2018

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

#### Explanation:

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

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

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

Hence it's a right triangle with $\hat{C} = \frac{\pi}{2} = {90}^{\circ}$

$\sin A = \frac{o p p}{h y p} = \frac{b}{c} = \frac{7}{25}$

$\hat{A} = {\sin}^{-} 1 \left(\frac{7}{25}\right) = {0.2838}^{c} \mathmr{and} {16.26}^{\circ}$

$\therefore \hat{B} = \pi - \frac{\pi}{2} - 0.2838 = {1.287}^{c} \mathmr{and} = {73.74}^{\circ}$

$\textcolor{red}{\text{Verification : }} \sin B = \frac{o p p}{h y p} = \frac{24}{25}$

$\hat{B} = {\sin}^{-} 1 \left(\frac{24}{25}\right) = {1.287}^{c} \mathmr{and} = {73.74}^{\circ}$