Question

in triangle xyz right angled at y if xy=5cm , xz = 5

in root2 cm then determine angla x and y

Answer 1

refer to the attachment

Answer 2

The measure of angle x is 45° and measure of angle y is 90°.

Step-by-step explanation:

Given information: xyz right angled at y if xy=5cm , xz = 5.

Angle y is a right angle it means the measure of angle y is 90°.

According to Pythagoras theorem,

$hypotenuse^2=base^2+perpendicular^2$

$(xz)^2=(xy)^2+(yz)^2$

$(5\sqrt{2})^2=(5)^2+(yz)^2$

$50=25+(yz)^2$

$50-25=(yz)^2$

$25=(yz)^2$

Taking square root on both sides.

$5=yz$

In a right angle triangle,

$\sin \theta=\dfrac{Opposite}{Hypotenuse}$

Using this, we get

$\sin x=\dfrac{yz}{xz}$

$\sin x=\dfrac{5}{5\sqrt{2}}$

$\sin x=\dfrac{1}{\sqrt{2}}$

$\sin x=\sin(45^{\circ})$

$x=45^{\circ}$

Therefore, the measure of angle x is 45° and measure of angle y is 90°.

#Learn more

In ΔABC, m∠B=90, AC+BC=25 and AB=5, determine the value of sinA, cosA and tanA.

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