Question

In AVWX, the measure of ZX=90°, XW = 3, WV = 5, and VX = 4. What is the value of

the tangent of ZW to the nearest hundredth?

Answer 1

We can use the Law of Cosines to find the value of ZW. The Law of Cosines states that:

c^2 = a^2 + b^2 - 2ab * cos(C)

where c is the length of the side opposite the angle C, and a and b are the lengths of the other two sides. In this case, we can use ZW as c, WV as a, and XW as b:

ZW^2 = WV^2 + XW^2 - 2 * WV * XW * cos(ZX)

Substituting in the values we know:

ZW^2 = 5^2 + 3^2 - 2 * 5 * 3 * cos(90)

cos(90) = 0, so the equation becomes:

ZW^2 = 5^2 + 3^2

ZW^2 = 25 + 9

ZW^2 = 34

ZW = sqrt(34)

ZW = approximately 5.83

Now that we have the length of ZW, we can find the tangent of ZW by dividing the length of the side opposite ZW (WV) by the length of the side adjacent to ZW (XW):

tan(ZW) = WV / XW

tan(ZW) = 5 / 3

tan(ZW) = 1.67

Rounding to the nearest hundredth, the tangent of ZW is approximately 1.67.

Answer 2

The tangent of angle W to the nearest hundredth is 1.33

Trigonometric ratio is the ratio between the sides of a right triangle.

Since it has been given that angle X is 90°, then the triangle is right triangle.

This means that VX will be the opposite to the acute angle W and XW will be the opposite.

Tan W = opp/adj

opp = 4

adj = 3

Therefore;

Tan W = 4/3

= 1.33

Therefore, the value of the tangent of angle W is 1.33