Question

A parallelogram has side lengths of 13 and 17 and an
angle that measures 64º.
What is x, the length of the diagonal, to the nearest
whole number?

Answer 1

Answer:

$x = 16$

Step-by-step explanation:

x = length of diagonal, can be calculated using the Law of Cosines as explained below:

a² = b² + c² - 2bc(cosA),

Where,

a = x

b = 17

c = 13

A = 64°

Plug in the values into the formula:

$x^2 = 17^2 + 13^2 - 2(17)(13)*cos(64)$

$x^2 = 289 + 169 - 442*0.4384$

$x^2 = 458 - 193.77$

$x^2 = 264.23$

$x = \sqrt{264.23}$

$x = 16.255$

Length of diagonal, $x = 16$ (to nearest whole number)