What is the answer for X (geometry)

Question

asked Oct 25, 2021 54.0k views

1 Answer

Daniel Ballinger · Answer 1 · 2021-10-29T22:23:48+0000

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In the lower triangle, one of the angles of which is 45 degrees, we know:

In the triangle, the side facing the angle 45° is √2 / 2 times the hypothenuse.

Thus ;

$10 = hypothenuse * ( √(2) )/(2) \\$

$hypothenuse * ( √(2) )/(2) = 10 \\$

Multiply sides by 2

hypothenuse * √(2) = 2 * 10

Divide sides by √2

$hypothenuse = (2 * 10)/( √(2) ) \\$

$hypothenuse = ( √(2) * √(2) * 10 )/( √(2) ) \\$

hypothenuse = 10 √(2)

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The common side of the triangles is hypothenuse for both.

$hypothenuse * \cos(60) = x$

$10 √(2) * (1)/(2) = x \\$

$x = (2 * 5 √(2) )/(2) \\$

x = 5 √(2)

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The correct answer is the Third Option .

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