Question

100 points big answer
If tan f° = two over one and the measure of segment YW is 8 units, what is the measure of segment XW? triangle XYW in which angle W is a right angle, angle X measure f degrees, and angle Y measures d degrees 2 units 4 units 7 units 8 units

Answer 1

Answer :

• 4 units

Explanation :

• tanθ = opposite/adjacent

here,

• opposite side of angle X = 8 units
• adjacent side of angle X = XW

plugging in the values,

• 2/1 = 8 units/XW
• XW = 8 units/2
• XW = 4 units

therefore,the measure of segment XW is 4 units.

Answer 2

Answer:

$\sf \overline{XW}=4$

Step-by-step explanation:

The tangent trigonometric ratio is the ratio of the side opposite the angle to the side adjacent the angle in a right triangle.

$\boxed{\begin{array}{l}\underline{\textsf{Tangent trigonometric ratio}}\\\\\sf \tan(\theta)=\dfrac{O}{A}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{ \theta is the angle.}\\\phantom{ww}\bullet\;\textsf{ O is the side opposite the angle.}\\\phantom{ww}\bullet\;\textsf{ A is the side adjacent the angle.}\end{array}}$

In triangle XYW, the side opposite angle f° is YW, and side adjacent angle f° is XW. Therefore, we can express tan f° as follows:

$\sf \tan f^{\circ}=\dfrac{\overline{YW}}{\overline{XW}}$

Given that $\sf \overline{YW}$ is 8 units, then:

$\sf \tan f^{\circ}=\dfrac{8}{\overline{XW}}$

We are also told that the ratio of tan f° = 2 / 1, so we can equate the two ratios (since they both equal tan f°), and solve for $\sf \overline{XW}$:

$\sf \dfrac{2}{1}=\dfrac{8}{\overline{XW}}$

Multiply both sides by $\sf \overline{XW}$:

$\sf 2\;\overline{XW}=8$

Divide both sides by 2:

$\sf \overline{XW}=4$

Therefore, the measure of segment XW is:

$\LARGE\boxed{\boxed{\sf \overline{XW}=4}}$