Answer:
A:102
Step-by-step explanation:
We are given that the points A(0,0),B(0,4a-5) and C(2a-+1,2a+6) form a triangle.
If angle ABC=
We have to find the area of triangle ABC
If angle ABC= 90 degree
From given below figure




Substitute the values then we get
B(0,17) and C (12,17)
Distance formula

AB=
BC=
BC=
units
Area of triangle =
Substitute the values
Then we get
Area of triangle ABC=
Area of triangle ABC=102 square units
Answer: A: 102
The boat's travel from when it was first noticed until it stopped is 554.89 ft.
<h3>What is trigonometry?</h3>
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.
From the given information we can draw a right-angle triangle.
14°52' = 14 + 0.86 = 14.86 degree
45°10' = 45 + 0.16 = 45.16 degree
In the right-angle triangle ACD
tan14.86 = 200/AC
AC = 753.772 ft
In the right-angle triangle DBC:
tan45.16 = 200/CB
CB = 198.886 ft
AB = AC - CB
AB = 753.772 ft - 198.886 ft
AB = 554.886 ≈ 554.89 ft
Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.
Learn more about trigonometry here:
brainly.com/question/26719838
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