Question

In ΔXYZ, ∠Y=90° and ∠X=40°. ∠ZWY=51° and XW=600. Find the length of ZY to the nearest integer.

Answer 1

In a right triangle XYZ with angles X and Y given, we can use trigonometry to find the length of ZY. Using the tangent function, we can set up an equation and solve for ZY with the given values. The length of ZY is approximately 800 units.

Step-by-step explanation:

In the given triangle XYZ, angle Y is 90° and angle X is 40°. Angle ZWY is 51° and the length of XW is 600 units. We need to find the length of ZY to the nearest integer.

To find the length of ZY, we can use the trigonometric relationship in a right triangle. Since angle Y is 90°, triangle XYZ is a right triangle. We can use the trigonometric function tangent (tan) to find the length of ZY.

Given that tan angle ZWY = opposite/adjacent, we have:

tan 51° = ZY/XW

Substituting the values, we get:

tan 51° = ZY/600

Now, we can solve for ZY by multiplying both sides of the equation by 600:

ZY = 600 * tan 51°

Calculating the value, we find that ZY is approximately 800 units.

Answer 2

The image of the triangle is missing so i have attached it.

Answer:

ZY ≈ 391

Step-by-step explanation:

From the attached image, ∠WZY = 180 - (51 + 90) = 39°. Because ΔWYZ is a right angle triangle and sum of angle in a triangle = 180°

Now, similarly ∠XZY = 180 - (40 + 90) = 50°

Using sine rule, we can find WZ;

WZ/sin 40 = XW/sin 50

We are given XW = 600

Thus;

WZ = (600 × sin 40)/sin 50

WZ = 503.5

Now, ZY can be found using trigonometric ratios;

ZY/WZ = sin 51°

Thus;

ZY = 503.5 × sin 51

ZY ≈ 391