Question

Please help me! thanks

Answer 1

x = 5.41

Explanation:

To find the measure of side x, we can use the cosine trigonometric ratio:

`\boxed{\begin{array}{l}\underline{\textsf{Cosine trigonometric ratio}}\\\\\sf \cos(\theta)=(A)/(H)\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the angle.}\\\phantom{ww}\bullet\;\textsf{$A$ is the side adjacent the angle.}\\\phantom{ww}\bullet\;\textsf{$H$ is the hypotenuse (the side opposite the right angle).}\end{array}}`

In this case:

• θ = 78°
• A = x
• H = 26

Substitute the values into the cosine ratio:

`\cos (78^(\circ))=(x)/(26)`

Multiply both sides of the equation by 26 to isolate x:

`x=26\cos (78^(\circ))`

Evaluate using a calculator:

`x=5.40570396...`

Finally, round to the nearest hundreth:

`\Large\boxed{\boxed{x = 5.41}}`

Answer 2

The value of x is 5.41.

To find the measure of X in the given scenario, where X is the length of a side in a right-angled triangle and the angle opposite to it is
`\( 26^\circ \)`, the cosine function is utilized.

The cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse. In this case, the adjacent side is x and the hypotenuse is
`\( 78^\circ \)`. The cosine of an angle
`\( \theta \)`is given by the formula:

`\[ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \]`

For this problem:

`\[ \cos(26^\circ) = (x)/(78^\circ) \]`

To solve for x, rearrange the equation:

`\[ x = 78^\circ \cdot \cos(26^\circ) \]`

Using a calculator, evaluate
`\( \cos(26^\circ) \)`, and then multiply it by
`\( 78^\circ \)`to find x. Rounding to the nearest hundredth, the answer is approximately x = 5.41 .