Question

(50 points) What is the value of x in the triangle?

Enter your answer as a decimal. Round your final answer to the nearest hundredth.

Answer 1

x = 23.78 cm to the nearest hundredth

Explanation:

In a right-angled triangle:

The opposite "O" is the opposite side to the angle

The adjacent side "A" is adjacent side to the angle

The hypotenuse "H" is the long side that joins the 2 legs

For this triangle, we have:

angle = 18°

adjacent (A) = x

hypotensue (H) = 25

So we can use the trig formula:
`cos(\theta)=(A)/(H)`

Therefore,
`cos(18)=(x)/(25)`

Multiply both sides by 25: 25 cos(18) = x

Therefore, x = 23.77841291...

So x = 23.78 cm to the nearest hundredth