Answer:
Part 1: x = 6.2
Part 2: u = 3.46 and v = 2
Part 3: Altitude = 5.196
Step-by-step explanation:
Part 1:
From the given figure, we can write
[tex]\cos 59 = \frac{x}{12}[/tex]
⇒ x = 12 cos 59 = 6.18 ≈ 6.2 (Answer)
Part 2:
From the figure we can write [tex]\sin 60 = \frac{u}{4}[/tex]
⇒ u = 4 sin 60 = 3.46 (Answer)
And [tex]\cos 60 = \frac{v}{4}[/tex]
⇒ v = 4 cos 60 = 2 (Answer)
Part 3:
Perimeter of the equilateral triangle is 18.
So, if each side is a, then 3a = 18
⇒ a = 6
Now, if we draw an altitude to the equilateral triangle then it will bisect the base perpendicularly.
If the altitude is x,
Therefore, applying Pythagoras Theorem we get
x² + 3² = 6²
⇒ x² = 27
⇒ x = 5.169 (Answer)
