Question

Find u. See image below.

Answer 1

The value of u is 2 in the given right-angled triangle.

The given figure is a right-angled triangle with hypotenuse 'u' and the other two sides as $\sqrt{2}$ and v.

We have to find the value of 'u' using Pythagoras theorem or trigonometric identities.

What is Pythagoras theorem?

It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In a right-angled triangle ABC, if

BC = hypotenuse

AC and AB are the other two sides then,

$BC^2 = AC^2 + AB^2$.

For this problem, we can find the value of u by using trigonometric identities.

From the figure, we have an angle of 45°.

Consider Cos 45°.

Cos Ф = base / hypotenuse

Cos 45° = $\sqrt{2}$ / u ...........(1)

From trigonometric identities of cosine.

We have,

Cos 45° = 1 / $\sqrt{2}$............(2)

From (1) and (2)

We get,

1 / $\sqrt{2}$ = $\sqrt{2}$ / u

u = 2.

Thus the value of u is 2 in the given right-angled triangle.

Learn more about Pythagoras's theorem application here:

brainly.com/question/11687813

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