Question

25 POINTS WILL MARK RIGHT ANSWER AS BRAINLIEST! What is the value of x to the nearest tenth?

Answer 1

Answer:

The value of x is 2.5 to the nearest tenth

Step-by-step explanation:

* Lets revise the trigonometry functions

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Now lets solve the problem

∵ x is opposite to the angle of measure 23°

∵ 6 is adjacent to the angle of measure 23°

∴ tan(23°) = x/6 ⇒ × 6 to both sides

∴ x = 6 × tan(23°) = 2.5

* The value of x is 2.5 to the nearest tenth

Answer 2

Answer: $x=2.5$

Step-by-step explanation:

You need to remember the identity:

$tan\alpha=\frac{opposite}{adjacent}$

You can identify in the figure that for the angle 67°:

$\alpha=67\°\\opposite=6\\adjacent=x$

Then you need to substitute these values into  $tan\alpha=\frac{opposite}{adjacent}$ and solve for "x":

$tan(67\°)=\frac{6}{x}\\\\xtan(67\°)=6\\\\x=\frac{6}{tan(67\°)}\\\\x=2.5$