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Answer:
The length of the rope between the boat and the dock is of 30 feet.
Step-by-step explanation:
Given:
tan(40) ≈ 0.839
Angle of depression = 40 (deg)
Distance between boat and the floor of the ocean = 25.17 feet
If we look into the diagram we can see that,they form 2 right angled triangle.
Where we can say that :
Distance between boat and dock = Rope's distance = Base of the triangle.
Let the length of the rope be 'x' feet.
Considering the dotted triangle:
⇒
⇒
⇒
⇒
⇒
⇒
Length of the rope between the boat and the dock is 'x' = 30 feet.
There is only one triangle possible having angle 50, 50, 80.
<h3>What is isosceles triangle?</h3>
An Isosceles Triangle has the following properties:
- Two sides are congruent to each other.
- The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle.
- The two angles opposite to the equal sides are congruent to each other.
It is given that, 2 angles of a triangle as:
∠1 = 50°
∠2 = 80°
Now we know the Angle sum property of a triangle that sum all three interior angle in a triangle is .
i.e., ∠1+∠2+∠3= .
So, 50° +80°+ ∠3 =
∠3 = 50°
As two angles of the triangle are equal that means it is a isosceles triangle.
There is no possibility of getting a right angles triangle.
Hence, there is only one triangle possible with these measurements .
Learn more about triangles here:
#SPJ1