Question

Fill in the blank.

Answer 1

Answer:

Part 1) $x=44.80\ units$

Part 2) $y=56.85\ units$

Step-by-step explanation:

Part 1) Find the value of x

we know that

In the right triangle of the figure

The tangent of angle of 52 degrees is equal to divide the opposite side to the angle of 52 degrees (x units) by the adjacent side to the angle of 52 degrees (35 units)

$tan(52\°)=x/35$

Solve for x

$x=(35)tan(52\°)$

$x=44.80\ units$

Part 2) Find the value of y

we know that

In the right triangle of the figure

The cosine of angle of 52 degrees is equal to divide the adjacent side to the angle of 52 degrees (35 units) by the hypotenuse (y units)

$cos(52\°)=35/y$

Solve for y

$y=35/cos(52\°)$

$y=56.85\ units$

Answer 2

Answer:

x = 56.85 units and y = 44.80 units.

Step-by-step explanation:

From the given figure it is clear that the given triangle is a right angle triangle.

According to the angle sum property of triangle the sum of interior angle of a triangle is 180°.

$z^{\circ}+90^{\circ}+52^{\circ}=180^{\circ}$

$z^{\circ}+142^{\circ}=180^{\circ}$

$z^{\circ}=180^{\circ}-142^{\circ}$

$z^{\circ}=38^{\circ}$

Law of Sine:

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

Using Law of Sine we get

$\dfrac{x}{\sin 52^{\circ}}=\dfrac{y}{\sin 90^{\circ}}=\dfrac{35}{\sin 38^{\circ}}$

$\dfrac{x}{\sin 52^{\circ}}=\dfrac{35}{\sin 38^{\circ}}$

$x=\dfrac{35}{\sin 38^{\circ}}\times \sin 52^{\circ}$

$x\approx 44.80$

The value of x is 44.80 units.

$\dfrac{y}{\sin 90^{\circ}}=\dfrac{35}{\sin 38^{\circ}}$

$y=\dfrac{35}{\sin 38^{\circ}}\times \sin 90^{\circ}$

$y\approx 56.85$

Therefore, the value of y is 56.85 units.